Josh, Ben and Rick have 70 marbles altogether. The ratio of the number marbles Josh has to the number of marbles Rick has is 1: 2. However, Ben has 15 marbles fewer than Rick. How many marbles does Ben have?

Answers

Answer 1

Answer:

Ben has 19 marbles

Step-by-step explanation:

First taking that josh and ricks ratio is 1:2, this would set up in an equation as [tex]2j = r[/tex] and with ben having 15 less than rick, his formula would be [tex]r = b + 15[/tex] as well as the total of all the boys marbles together being this [tex]j+r+b=70[/tex]

Now we put all of these equations into a set to answer them.

[tex]2j = r\\ r = b + 15\\j+r+b=70[/tex]

First we solve for j

[tex]2j = r\\ j=\frac{1}{2} r[/tex]

Then substitute j

[tex]j+r+b=70\\ \frac{1}{2}r+r+b=70\\ 2b+3r=140[/tex]

Then simplify and multiply by 2 to even out

[tex]r = b + 15\\ -b+r=15\\2b+3r=140[/tex]

Now eliminate the b variable and combine equations

[tex]2b+3r=140\\-2b+2r=30[/tex]

[tex]5r=170[/tex]

Now divide and solve for r

[tex]5r=170\\r=34[/tex]

Now we know Rick has 34 marbles of the 70 marbles, so we can substitute his number back into the original equation

[tex]-b+34=15\\b=19[/tex]

Now we know Ben has 19 marbles of the remaining 36, and can substitute his number as well

[tex]j=\frac{1}{2}(34)\\j=17[/tex]

And now we know how much everyone has, to check we rewrite all the equations with their respective numbers

[tex]11+34+19=70\\2(17)=34\\34=19+15[/tex]

[tex]70=70\\34=34\\34=34[/tex]

Which means the ordered pairing of (b, j, r) is (19, 17, 34)


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Answers

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Step-by-step explanation:

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