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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?

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GodSaveTheMeme
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.
calculista

Answer:

The youngest brother has ----> [tex]\$18[/tex]

The third brother has -------->  [tex]\$54[/tex]

Step-by-step explanation:

Let

x-----> the total money

we know that

The oldest brother has ----> [tex]\frac{3}{5}x[/tex] -----> [tex]\frac{6}{10}x[/tex]

The youngest brother has ----> [tex]\frac{1}{10}x[/tex]

The third brother has ----> [tex]1-(\frac{6}{10}x+\frac{1}{10}x)=\frac{3}{10}x[/tex]

[tex]\frac{3}{5}x=108[/tex] ----> given problem

Solve for x

[tex]x=108*5/3=\$180[/tex]

so

The youngest brother has ----> [tex]\frac{1}{10}(180)=\$18[/tex]

The third brother has -------->  [tex]\frac{3}{10}(180)=\$54[/tex]

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