SOLUTION: The difference between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number

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Question 257748: The difference between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number
Found 2 solutions by checkley77, dabanfield:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X-Y=15 OR X=Y+15
3X-2Y=58
3(Y+15)-2Y=58
3Y+45-2Y=58
Y=58-45
Y=13 ANS. FOR THE SMALLER NUMBER.
X-13=15
X=15+13
X=28 ANS. FOR THE LARGER NUMBER.
PROOF:
3*28-2*13=58
84-26=58
58=58

Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between two numbers is 15. When twice the smaller number is subtracted from three times the larger number, the difference is 58. What is the larger number
Let x be the smaller and y the larger number.
Then:
1.) y - x = 15 and
2.) 3*y - 2*x = 58
From 1.) we have y = x + 15. Substituting x + 15 for y in 2.) we have:
3*(x + 15) - 2*x = 58
3*x + 45 - 2*x = 58
x = 58 - 45
x = 13
Since y = x + 15:
y = 13 + 15
y = 28