SOLUTION: Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more then Jack's age. Find Jack and Sam's age.

Click here to see ALL problems on Miscellaneous Word Problems

Question 208425: Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more then Jack's age. Find Jack and Sam's age.
Found 2 solutions by algebrapro18, MathTherapy:
Answer by algebrapro18(249) (Show Source):
You can put this solution on YOUR website!
Well this is a system of equations problem so lets start by setting up the system.

Let j = jacks age and s = sam's age for this problem.

Then taking it one line at a time we see taht Sam is 10 years older than Jack or in equation form s = 10+j. We also kow that Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age. In equations this becomes 2s-6j = 7+j.

So we have our system its:

s = 10+j
2s-6j = 7+j

Now since we know what s equals we can just substitute that into the second
equation and solve for j

2s-6j = 7+j
2(10+j)-6j = 7+j
20+2j-6j = 7+j
20-4j = 7+j
20 = 7 + 5j
13 = 5j
j = 2.6 years

so now that we know that jack is 2.6 years old we plug that into the first equation and find that sam is 12.6 years old.

I will leave the checking up to you.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more then Jack's age. Find Jack and Sam's age.

Let Jack's age be J
Since Sam is 10 years older than Jack, then Sam is J + 10 years old

Since twice Sam's age subtracted from 6 times Jack's age is 7 more then Jack's age, then we have:

6J - 2(J + 10) = J + 7

6J - 2J - 20 = J + 7

6J - 2J - J = 7 + 20

3J = 27

= 9

Therefore, Jack is years old, and Sam is (9 + 10) years old.