SOLUTION: if you add jasons and heathers age you get 51. jason is 9 years younger then twice heathers age. find out both ages.

Question 903143: if you add jasons and heathers age you get 51. jason is 9 years younger then twice heathers age. find out both ages.

Found 2 solutions by AlgebraLady88, tutoringisfun2:
Answer by AlgebraLady88(44) (Show Source): You can put this solution on YOUR website!
If you add Jason and Heather's age, you get 51.
Let's write this algebraically.
That would be J+H = 51
Jason is 9 years younger than twice Heather's age.We can also write this algebraically.
J= 2H -9
Now , we have two equations : J+H= 51 and J= 2H-9
We can focus on finding out either Heather or Jason's age first. Finding one will help us find the other one, so order does not matter. For this example, I will find out Heather's age first.
From the equation J+H= 51 , I get J= 51-H
I substitute J= 51-H in the equation J= 2H-9
51-H = 2H-9
-H-2H=-9-51
-3H =-60
(Divide both sides with -3) gives us H= 20
If Heather is 20, Jason is 31 as both added up gives us 51.
Let's check. Twice Heather's age is 40. At 31, Jason is 9 years younger than twice Heather's age.

Answer by tutoringisfun2(2) (Show Source): You can put this solution on YOUR website!
first you write down the information given in the problem above.
J= Jason's age
H=Heather's age
in the problem it says that if you add Jason's age and Heather's age you get 51. So the 1st equation that we write is: J+H=51
We also know from the information stated in the problem that Jason's age is equal to twice Heather's age - 9 years. From this information we can get the equation J=2H-9
Now substitute 2H-9 for J and solve the equation:
2H-9+H=51
combining like terms we get 3H-9=51
we need to get H by itself. In order to do that you have to add 9 to both sides of the equation, the -9 and the +9 on the left side cancel each other out so you are left with
3H=51+9
add 51+9 and you get 60 so 3H=60
in order to get H by itself you have to divide by 3. 60/3=20
Therefore H=20. So heather is 20 years old.
To find Jason's age we take H which is 20 and plug it into the equation J=2H-9 as follows:
J=2(20)-9 Solving this equation gives us the following:
J=40-9
J=31. So Jason is 31. You can check your answer by plugging both values for H and J into the original equation J+H=51.
31+20=51. This is a true statement, so the answer is correct.
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