SOLUTION: The ages of John and Mary total 27 years. Mary's age plus twice John's age is 40. How old is each person? j+m = 27 m+2j = 40 Now I'm stuck...

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Question 1097525: The ages of John and Mary total 27 years. Mary's age plus twice John's age is 40. How old is each person?
j+m = 27
m+2j = 40
Now I'm stuck...
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Nice job so far on getting the correct equations set up.

Let's solve the first equation for j
Subtract 'm' from both sides to get...
j+m = 27
j+m-m = 27-m
j = 27-m

Now we'll plug this into the second equation.
Essentially this means we replace every copy of 'j' with 27-m
m + 2j = 40
m + 2*( j ) = 40
m + 2*( 27-m ) = 40 ... replace j with 27-m

Now we solve for m
m + 2*( 27-m ) = 40
m + 2*( 27 ) + 2*( -m ) = 40
m + 54 - 2m = 40
1m - 2m + 54 = 40
-1m + 54 = 40
-1m + 54 - 54 = 40 - 54
-1m = - 14
-1m/(-1) = - 14/(-1)
m = 14

Use the value of m to get the value of j
j = 27-m
j = 27-14
j = 13
In summary, we get m = 14 and j = 13 which means that
Mary is 14 years old. John is 13 years old.

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Check:
Let's check the first equation
j+m = 27
13+14 = 27
27 = 27
that equation works

Do the same for the second equation
m+2*j = 40
14+2*13 = 40
14+26 = 40
40 = 40
that equation works as well

The answer has been confirmed.