SOLUTION: The sum of two numbers is 32; the larger number is 12 greater than twice the smaller. What are the 2 numbers?

Question 290166: The sum of two numbers is 32; the larger number is 12 greater than twice the smaller. What are the 2 numbers?
Found 3 solutions by bcampbell23669, MathTherapy, richwmiller:
Answer by bcampbell23669(14)   (Show Source): You can put this solution on YOUR website!
The Answer is : 10, 22
Start with 32. We need to have 12 greater than twice the smaller number. So we need to first subtract 12 from 32.
32-12 = 20. Then we need to divide that by two to get the smaller # 20/2 = 10
Subtract 10 from 32 to get the larger #.
32-10 = 22
Answer: 10, 22
Hope this helps! :-) Good luck!
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 32; the larger number is 12 greater than twice the smaller. What are the 2 numbers?

Let the larger number be L, and the smaller S

Then L + S = 32 (their sum is 32)

Also, L = 2S + 12 (given that the larger, or L is 12 greater than twice the smaller, or S)

We now have:

L + S = 32 ------(i)
L - 2S = 12 ----- (ii)

Subtract eq (ii) from eq (i) to get: 3S = 20

Therefore, S =

Substitute this value for S in eq (i) to get:

L = or

Therefore, L, or the larger number is , while S, or the smaller number is: .
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
10 and 22 don't work
because the 22 is not 12 greater than twice the smaller
it is only 12 greater than the smaller.
32-12=20
20/3=smaller
and 40/3+12= larger
6 2/3
12 4/3=13 1/3+12=25 /13
25 1/3+6 2/3=32
check
25 1/3-12=13 1/3
13 1/3 is twice 6 2/3
ok
Answer
25 1/3
6 2/3
which is equal to maththerapy's answer since
20/3=6 2/3
76/3=25 1/3
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