Question

Three brothers have some money. The oldest has 3/5 of the total, and the youngest has 1/10 of the total. If the oldest brother has $108, how much do each of the other brothers have?

Answer 1

First, let's get rid of the unneeded info.

Oldest brother has $108 (3/5 the total)
Youngest brother has $x (1/10 the total)

Next let's find out the total. We do this by multiplying the oldest brothers money by 5/3 (the reciprocal).

108 × (5/3) = 180.

So the total amount of money is $180.

Finally, do 180 × (1/10) to find the youngest brother's amount.

180 × (1/10) = 18.

The youngest brother has $18.

Answer 2

The youngest brother has ---->
`\$18`

The third brother has -------->
`\$54`

Explanation:

Let

x-----> the total money

we know that

The oldest brother has ---->
`(3)/(5)x` ----->
`(6)/(10)x`

The youngest brother has ---->
`(1)/(10)x`

The third brother has ---->
`1-((6)/(10)x+(1)/(10)x)=(3)/(10)x`

`(3)/(5)x=108` ----> given problem

Solve for x

`x=108*5/3=\$180`

so

The youngest brother has ---->
`(1)/(10)(180)=\$18`

The third brother has -------->
`(3)/(10)(180)=\$54`