SOLUTION: Paul is 12 years older than Colin. Caroline is 3 years younger than Colin. If the total of their ages is 87, how old is the youngest of them?

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Question 1151157: Paul is 12 years older than Colin. Caroline is 3 years younger than Colin. If the total of their ages is 87, how old is the youngest of them?

Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) (Show Source):
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x = Paul's current age
y = Colin's current age
z = Caroline's current age

x = y+12 because Paul is 12 yrs older than Colin
z = y-3 because Caroline is 3 yrs younger than Colin

Solve x = y+12 for y
x = y+12
y+12 = x
y+12-12 = x-12 ... subtract 12 from both sides
y = x-12

Substitute that into z = y-3
z = y-3
z = x-12-3 ... replace y with x-12
z = x-15
This tells us Caroline is 15 years younger than Paul.

The three ages add to 87
x+y+z = 87
x+x-12+z = 87 ... plug in y = x-12
x+x-12+x-15 = 87 ... plug in z = x-15
3x-27 = 87
3x-27+27 = 87+27 ... add 27 to both sides
3x = 114
3x/3 = 114/3 ... divide both sides by 3
x = 38
Paul is 38 years old currently.

Use this to find the value of y.
y = x-12
y = 38-12 ... plug in x = 38
y = 26
Colin is currently 26 years old.

Use the same x value to find the value of z.
z = x-15
z = 38-15 ... plug in x = 38
z = 23
Caronline is currently 23 years old.
Alternatively, you can use the value of y to find the value of z.
z = y - 3
z = 26 - 3
z = 23

To summarize,
Paul is 38 years old
Colin is 26 years old
Caroline is 23 years old

Answer: The youngest (Caroline) is 23 years old

Check:
x+y+z = 87
38+26+23 = 87
64+23 = 87
87 = 87
We get a true equation, so the answer is confirmed.

Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!

PERSON AGE Paul c+12 Colin c Caroline c-3 Total 87

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-------------------Colin's age

The youngest is Caroline, .