1. ## [SOLVED] word problem

Four boys bought a boat for $60 . The first boy paid one half of the sum of the amounts paid by the other boys. The second boy paid one third of the sum of the amounts paid by the other boys and the third boy paid one-fourth of the sum of the amounts paid by the other boys.How much did the fourth boy pay? 2. Originally Posted by Mr.Green Four boys bought a boat for$60 . The first boy paid one half of the sum of the amounts paid by the other boys. The second boy paid one third of the sum of the amounts paid by the other boys and the third boy paid one-fourth of the sum of the amounts paid by the other boys.How much did the fourth boy pay?
Ok first let's write everything down we can into equations. Let $\displaystyle B_{1},B_{2},B_{3},B_{4}$ each stand for the price that each boy paid. From the first sentence,$\displaystyle B_{1}+B_{2}+B_{3}+B_{4}=60$. Now for the rest.

"The first boy paid one half of the sum of the amounts paid by the other boys."

$\displaystyle B_{1}= \frac{1}{2} \left( B_{2}+B_{3}+B_{4} \right)$. See how that worked?

For the second boy, it's very similar just one-third of the total of the others.

$\displaystyle B_{2}= \frac{1}{3} \left( B_{1}+B_{3}+B_{4} \right)$

And for the third,

$\displaystyle B_{3}= \frac{1}{4} \left( B_{1}+B_{2}+B_{4} \right)$

So, now we have 4 variables and 4 equations and we can solve for each of them.

You with me so far?

3. Originally Posted by Jameson
Ok first let's write everything down we can into equations. Let $\displaystyle B_{1},B_{2},B_{3},B_{4}$ each stand for the price that each boy paid. From the first sentence,$\displaystyle B_{1}+B_{2}+B_{3}+B_{4}=60$. Now for the rest.

"The first boy paid one half of the sum of the amounts paid by the other boys."

$\displaystyle B_{1}= \frac{1}{2} \left( B_{2}+B_{3}+B_{4} \right)$. See how that worked?

For the second boy, it's very similar just one-third of the total of the others.

$\displaystyle B_{2}= \frac{1}{3} \left( B_{1}+B_{3}+B_{4} \right)$

And for the third,

$\displaystyle B_{3}= \frac{1}{4} \left( B_{1}+B_{2}+B_{4} \right)$

So, now we have 4 variables and 4 equations and we can solve for each of them.

You with me so far?
thanks a lot to u really great help i can do the remaining steps

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