SOLUTION: Hi, here is a problem I've been stuck on, please help, if possible! In 7 years, Maria will be 4 times as old as Angelica will be then. The sum of their ages is now 71. How old w

Question 194189This question is from textbook academic systems elementary algebra
: Hi, here is a problem I've been stuck on, please help, if possible!
In 7 years, Maria will be 4 times as old as Angelica will be then. The sum of their ages is now 71. How old will each of them be in 5 years?
So far, I've got a chart like this:
Maria: In 7 years: 4(x+7). In 5 Years: x+5 (not sure if Maria is still 4 times older than Angelica in 5 years?)
Angelica: In 7 years: x+7. In 5 Years: x+5. =71
I put the equation together like this:
4(x+7) - (x+5)= 71
4(x + 28) - (x+5)= 71
4x + 28 - (x+5) = 71
4x - x +28 - 5 = 71
3x + 23 = 71
3x =48
X = 16
The solution I get is 16, but the answer at the back of the book says Angelica is 15, and Maria is 66! What did I do wrong, and what is the correct way to solve? Any help would be great, thanks!
Leanne RainThis question is from textbook academic systems elementary algebra

Answer by stanbon(57387) (Show Source):
You can put this solution on YOUR website!
In 7 years, Maria will be 4 times as old as Angelica will be then. The sum of their ages is now 71. How old will each of them be in 5 years?
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NOW DATA:
Let Maria be "M" yrs. old
Then Angel is "71-M"
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7 yrs from NOW DATA:
Maria will be "M+7"
Angel will be "71-M+7" = 78-M
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Equation based on 7 yrs. from NOW DATA:
M+7 = 4(78-M)
M+7 = 312 - 4M
5M = 305
M = 61 (Maria's age NOW)
Angel = 71-M = 71-61 = 10 (Angel's age NOW)
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5 yrs from NOW
Maria will be 61+5 = 65
Angel will be 10+5 = 15
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Cheers,
Stan H.