word problem: The sum of the current ages of Angie and....

[learning]

I cannot solve this one!!!! :x

The sum of the current ages of Angie and her mother are 64 years. In eight years, Angie will be three fifths as old as her mother at that time. Find the present ages of Angie and her mother.

I tried it this way:

3/5(64-x)+8=64
192/5 - 3/5x + 8 = 64
192 - 3x + 40 = 320
232 - 3x = 320
-3x = 88
x = 29

The answer in the math book says:
Angie 22
Mother 42
What am I doing wrong??

 

[tkhunny]

Re: word problems

The sum of the current ages of angie and her mother are 64 years. In eight years, Angie will be three fifths as old as her mother at that time. Find the present ages of Angie and her mother.

Have you tried clear and precise definitions?

A = Angie's Age Now
M = Mom's Age Now

A+8 = Angie's Age Now 8 years from now
M+8 = Mom's Age Now 8 years from now

"The sum of the current ages of angie and her mother [is] 64 years."

A + M = 64

"In eight years, Angie will be three fifths as old as her mother at that time."

A+8 = (3/5)*(M+8)

Since, M = 64 - A, we have A+8 = (3/5)*((64-A)+8)

I am somewhat confident we won't be needing the fractions. Multiply by 5.

5(A+8) = 3*((64-A)+8)

Expand and Simplify

5A + 40 = 3*(64 - A + 8)
5A + 40 = 3*(72 - A)
5A + 40 = 216 - 3A

Add 3A

8A + 40 = 216

Subtract 40

8A = 176

Divide by 8

A = 22

How about 'M'?

I cannot follow what you were doing. Strive for clarity and readability.