Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing a total of $37.25. Zoe went into the same movie theater and bough 8 bags of popcorn and 9 pretzels, costing a total of $102.25. Write and solve a system of equations to determine the price of each bag of popcorn and the price of each pretzel.

Answers

Answer 1

Taking into account the definition of a system of linear equations, the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

x: price of each bag of popcorn. y: the price of each pretzel.

On one hand, Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing a total of $37.25.   This is expressed by 2x+5y= 37.25

Zoe went into the same movie theater and bough 8 bags of popcorn and 9 pretzels, costing a total of $102.25.  This is expressed by 8x+9y=102.25

So, the system of equations to solve is:

[tex]\left \{ {{2x+5y=37.25} \atop {8x+9y=102.25}} \right.[/tex]

There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.

So, isolating the variable x from the first equation:

2x+5y= 37.25

2x= 37.25 - 5y

x= (37.25 - 5y)÷2

x= 18.625 - [tex]\frac{5}{2}[/tex]y

Replacing in the second equation:

8×(18.625 - [tex]\frac{5}{2}[/tex]y)+9y=102.25

Solving:

8×18.625 - 8×[tex]\frac{5}{2}[/tex]y+9y=102.25

149 - 20y + 9y=102.25

149 -11y= 102.25

-11y= 102.25-149

-11y= -46.75

y= (-46.75)÷ (-11)

y= 4.25

Finally, replacing in x= 18.625 - [tex]\frac{5}{2}[/tex]y and solving you get:

x= 18.625 - [tex]\frac{5}{2}[/tex]×4.25

x= 18.625 - 10.625

x=8

Remembering that x represents the price of each bag of popcorn and y represents the price of each pretzel, you get that the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.

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Related Questions

Which of the following ordered pairs are solutions to the system of equations below?


Answers:
A.) (3.5, 5.8)
B.) (3.5, -5.8)
C.) (-3.5, -5.8)
D.) (-3.5, 5.8)

Answers

The answer is B. 3.5, -5.8

im having a mental breakdown can someone please just do this for me

Answers

the slopes of the original function y = |x| are m = 1 and m = -1 (m is the variable used to represent slope).

when you add a coefficient (number) in front of |x|, it will either make the slopes steeper or more flat. the larger the value of the coefficient, the steeper the slope will be (vice versa for a coefficient smaller than 1, which would make the slope more flat than the parent(original) function).

because these are absolute value functions, they will have two slopes. one slope for the end going up from left to right, and one for the end going down from left to right. this means that one slope must be positive and the other slope must be negative for each function.

with this in mind, the slopes of y = 2|x| are m = 2 and m = -2. the coefficient of 2 narrows the function by a factor of 2 (it is twice as narrow as the parent function). the same rules apply to y = 4|x| with the slopes of this function as m = -4 and m = 4 (it is 4 times narrower than the parent function).

with the fraction coefficients, the function is being widened. therefore, the slopes of y = 1/2 |x| are m = -1/2 and m = 1/2. the slopes of y = 1/5 |x| are m = -1/5 and m = 1/5.

Answer:

it only changes the magnitude.

for any general a let f(x) be =a|x| , a>0

so for any x say ±3 your function will throw out a×3.

33 + 55 = __ (3+5)
Help me with this

Answers

Answer:

11 I think and hi how are u ::):):):):):):):):):):):):):

11 I’m pretty sure I got it right

What is the perimeter of a rectangle whose length is twice the width? Width = 7 cm.

Answers

Answer:

42 cm is the perimeter

Step-by-step explanation:

Brainleast answer mo nalang

Answer:

P = 42 cm

Step-by-step explanation:

The perimeter (P) is the sum of the 4 sides of the rectangle with opposite sides being congruent.

Given width = 7 cm then length = 2 × 7 = 14

P = 7 + 7 + 14 + 14 = 42 cm

. .. . . . . . .. . .. . so easy

Answers

Answer: 7

Step-by-step explanation: if it's so easy, why do you need brainly? (not judging, just confused why you'd waste points)

A car is 12 feet long. Levi makes a scale model of the car at 1:8 of its actual size. How long is the model

Answers

Answer:

1.5 feet

Step-by-step explanation:

Answer:

1.5 feet or 3/2 feet

Step-by-step explanation:

can you help me solve 4^3/4^4?

Answers

Answer:

64/256

Step-by-step explanation:

4*4*4=64/4*4*4*4=256

Sure.

Answer: 0.25

Let’s break the question down.

4^3 (4 x 4 x 4) = 64.
4^4 (4 x 4 x 4 x 4) = 256.

64/256 = 0.25.

Write the equation of the line, in slope-intercept form, with the
following information:
slope:
3
point: (6,-1)

Answers

Answer:

y=3x-19

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=3(x-6)

y+1=3(x-6)

y=3x-18-1

y=3x-19

A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 12 ft.) Round to the nearest tenth of a foot.

Answers

Answer:

13.9 ft

Step-by-step explanation:

I have three bits of tinsel measuring the following: 2.3m, 45cm and 750mm. How long is my tinsel altogether in metres?​

Answers

100 cm= 1 meter 1,000 cm=meter
——————-
750 mm = 0.75 m
45 cm = 0.45 m
2.3 m
——————
Add and you should get 3.5. The tinsel is 3.5 meters long.

A 12 ounce Starbucks latte costs $3.36. What is the constant of proportionality that relates the cost in dollars, y, to the number of ounces, x, in a Starbucks latte?

Answers

Answer:

Y = X times 0.28

Step-by-step explanation:

1. You set it up as a proportionality

12/1 and 3.36/x

The x stands for how much money it takes to get 1 ounce

2. You do the old man line.

12 times x = 3.36 times 1

12x = 3.36

3. Now you divide 3.36 by 12

3.36 divided by 12

.28

4. You insert 0.28 into the problem

12 times 0.28 = 3.36

X = 0.28

So 1 ounce costs $0.28

So Y = X times 0.28

Answer:

Step-by-step explanation:

Samuel has 52 marbles in a bag. Fourteen are red, 13 are green and 25 are blue. If a marble is chosen at random, what is the probability that it is green?

Answers

.25
you can come to this conclusion by calculating 13/52

Does anybody know how to does this pleaseee helppppp. The first 2 my teacher did them for me but I’m still confused pleaseee helpppp

Answers

Answer:

below

Step-by-step explanation:

A triangle can only be a triangle if the two shortest sides add up to be greater than the longest side.

For example on the first one, the segments 1 2 and 3 will not make a triangle as 1 + 2 = 3 and if the two smallest sides of a triangle are equal to the longest side it will not be a triangle at all.

So to make this easy, out of the three numbers given: add the two smallest numbers. This number has to be greater than the third number given, and it cannot be equal.

For question three: 3+9 = 12

And 12 is greater than 11, therefore this can make a triangle.

A man has 25 sweets and his son has 55 sweets.find the number of sweets that the man has to give to his son so that his son would have 4times as many sweets as him.

Answers

Sweets man has to give is x
Man's sweets = 25 - x
The boy's sweets = 55 + x
This number is 4 times

55 + x = 4(25 - x)
55 + x = 100 - 4x
55 - 100 = -4x - x
-45 = - 5x
45 ÷ 5 = x
6.67 = x
6.67 ≈ 7
the man gives 7 sweets to the son so the son would have 4 times as much as the father

Answer:

9sweets

Step-by-step explanation:

sweets man has to give to his son=x

mans sweets=25-x

child's sweets=55=x

55+x=4(25-x)

55+x=100-4x

4x+x=100-55

5x=45

x=45/5

x=9

Answer: The man has to give nine sweets for his son to have four times as many sweets as him.

One serving of ice cream has 320 calories. If there are 6 servings in the container and you ate of the container, how many calories did you eat?

Answers

Answer: You ate 1920 calories

Step-by-step explanation:

It’s pretty simple,

all you have to do is multiply 6 by 320.

this then gets you 1920

Answer:

1920 calories

Step-by-step explanation:

6servings*320cal/servings = 1920cal (servings cancel)

PLEASE HELP QUESTION IN PICTURE

Answers

Answer:

y=4x+5

Step-by-step explanation:

3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.

Answers

Answer:

First term of the sequence is [tex]11[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference

We have

The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]

[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]

The sum of the third and fourth terms of the same sequence is [tex]7[/tex]

[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]

eqn 1 - eq2

[tex]4d=-12\\\\d=-3[/tex]

Substituting in eqn 1

[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]

First term of the sequence is [tex]11[/tex]

7363626x726=???? Helpppppp

Answers

Answer:

The answer is 5345992476

Step-by-step explanation:

20x+10x-8=0 solution set of equation

Answers

1. Combine like terms (30x -8 =0)
2. Isolate the variable (30x =8)
3. Divide both sides by the coefficient (x= 8/30)
4. Simplify (x= 4/15)

Answer:

0.2666666666

Step-by-step explanation:

20x+10x-8=0

first of all, you will +8 on both sides so there are no negative numbers onany side

20x+10x=8

now gather everything up

30x=8

divide everything by 30 now to get the value of 1x

30x/30=x

8/30=0.2666666666

Which expression is equivalent to 24 1/3?

Answers

Answer:

2∛3

Explanation:

∛24=(∛8)(∛3)=2∛3

Hopes This Helps :)

What is another word for change in y

Answers

When finding the slope of real-world situations, it is often referred to as rate of change. change in y Rate of change = change in x change in height change in time The average rate of change or a rider between 0 and 5 seconds is —24 ft/s. magnitude relation. Another synonym is "velocity".

Hope this helps

Zack buys some potatoes from a store. The potatoes cost $6.78 for 3 pounds. He wants to buy more vegetables, but at the same price per pound as the potatoes. Which of the following vegetables could Zack buy?

Answers

Answer:

well we dont know other vegis are going for each pound is 2.26 but any vegtable thats is going 2.26 per pound works  

Step-by-step explanation:

pls answer don’t scam

Answers

Answer:

y=x

step by step:

graph equation is y=mx+c

y intercept (c) is 0

gradient (m) is 1

gradient is represented as (m), so the equation is just y=1x, simplified-> y=x

Answer:

  money = 2×tickets

Step-by-step explanation:

For 1 ticket sold, $2 is collected. for 8 tickets sold, $16 is collected. The relationship appears to be proportional with a constant of proportionality of $2 per ticket.

The axes are labeled "money" and "tickets", so we can write the equation ...

  money = 2×tickets . . . . . where money is in dollars

__

If you like, you can use y to represent dollars collected, and x to represent tickets sold. Then the equation is ...

  y = 2x

WILL GOVE 50 POINTS AND BRAINLIEST PLZZZZZZZZZZZZZZZZZ HELP
Examine the diagram of a chloroplast.

Which choice best describes the function of the part labeled B?


enclosed space containing proteins used in ATP formation

membranes enclosing open space

layered stacks of membranes

fluid space that contains DNA, ribosomes, and other enzymes

Answers

Answer:

fluid space that contains DNA, ribosomes, and other enzymes

Step-by-step explanation:

B is points towards the "empty" space, meaning its Stroma.

Stroma defintion: involved in the synthesis of organic molecules from carbon dioxide and water or the fluid of the chloroplast surrounding the thylakoid membrane;

Let's look at the answer choices.

A. enclosed space containing proteins used in ATP formation

B. membranes enclosing open space

C. layered stacks of membranes

D. fluid space that contains DNA, ribosomes, and other enzymes

Obviously not C.

A is Synthase.

B is the whole thing.

It is D.

(BTW THIS IS MATH!! Not science!! Just in case you have more questions!)

Answer:

raw

Step-by-step explanation:

HELP PLZ I NEED THIS DONE ASAP

Answers

[tex]\text{Given that,}\\\\y^2 +9y +3 \\\\\text{when}~ y = -2,\\\\(-2)^2 +9(-2) +3 = 4-18+3 = 7 -18 = -11,[/tex]

Can someone please give me the (Answers) to this? ... please ...

Answers

The first answer is 22 , but I’m not sure about the rest

Simplify Simplify 6 - 23 + (-9 + 5) · 2.

Answers

Answer:

The answer is −42

What is the area of a rectangle with the following measurements:

Answers

Answer:

24x^5

Step-by-step explanation:

3 x 8 = 24

x multiplied by x^4 = x^5

(the exponents add to each other when multiplied)


Given that f(x) = 10 - 3x and g(x) = x-3/2 find the value of fg(4)

Answers

Answer:

-1

Step-by-step explanation:

(fg)(x) is the product of f(x) and g(x).

We can find (fg)(4) by first finding f(4) and g(4) and then multiplying the results together:

f(x) = 10 - 3x, so f(4) = 10 - 3(4) = -2, and

g(x) = x - 3/2, so g(4) = 4 - 3/2 = 1/2

Then (fg)(4) = (-2)(1/2) = -1

What is the product? (x 3)(2 x minus 1) 2 x squared minus 3 2 x squared 6 x 2 x squared 5 x minus 3 2 x squared 6 x minus 3.

Answers

The product of the function is 2x^2+ 5x - 3

We are to find the product of the functions x + 3 and 2x -1

let f(x) = x+ 3g(x) = 2x - 1

Taking the product:

f(x)g(x) = (x+3)(2x -1)

f(x)g(x) = x(2x) - x(1) + 3(2x) + 3(-1)

f(x)g(x) = 2x^2 - x + 6x - 3

f(x)g(x) = 2x^2+ 5x - 3

Hence the product of the function is 2x^2+ 5x - 3

Learn more on product of functions here: https://brainly.com/question/25638609

Answer:

c

Step-by-step explanation:

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