SOLUTION: Three Times the sum of two numbers is 45. Four times the sum of the same numbers is 60. The difference of the two numbers is nine. What are the numbers?

Question 951843: Three Times the sum of two numbers is 45. Four times the sum of the same numbers is 60. The difference of the two numbers is nine. What are the numbers?
Found 2 solutions by macston, MathTherapy:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
x and y are the numbers.
x-y=9 Add y to each side.
x=y+9
3(x+y)=45 Substitute for x
3((y+9)=y)=45 Divide each side by 3.
2y+9=15 Subtract 9 from each side.
2y=6 Divide each side by 2.
y=3 ANSWER 1: one of the numbers is 3.
x=y+9=3+9=12 ANSWER 2 The other number is 12.
CHECK:
4(x+y)=60
4(12+3)=60
4(15)=60
60=60

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Three Times the sum of two numbers is 45. Four times the sum of the same numbers is 60. The difference of the two numbers is nine. What are the numbers?

Since 3 times the numbers' sum is 45, and since 4 times the numbers' sum is 60, then the sum of the numbers is: 15.
With L being the larger and S being the smaller number, we get:
L + S = 15 ------- eq (i)
Also, L - S = 9 ------- eq (ii)
Add the 2 equations to get the value of L, the larger number
Substitute the value for L, or larger number into any of the 2 original equations to get S, the smaller number.
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