Question

Debra, Alan, and Shen have a total of 122 in their wallets. Alan has less than $7 Debra. She has 3 times what Alan has. How much do they have in their wallets?

Answer 1

Debra has $10.50, Alan has $3.50, and Shen has $108.

Explanation:

Set up a system of equations to represent the situation.

Let a represent Alan's money, d represent Debra's money, and s represent Shen's money.

1. a + d + s = 122

2. a = d - 7

3. d = 3a

Use equation's 1 and 2 alone to calculate a and d. Substitute Eq 3 into Eq 2 such that

a = 3a - 7

-2a = -7

a = $3.50

Use Alan's money to calculate Debra's money.

d = 3(3.5)

d = $10.50

Now use values of a and d to calulate Shen's money, given the total.

s + 3.5 + 10.5 = 122

s + 14 = 122

s = $108

So, Debra has $10.50, Alan has $3.50, and Shen has $108.