Question 182090: The difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. Find the numbers.
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! The difference between two numbers is 16.
Let's call the larger number x and the smaller number y.
x - y = 16
Five times the smaller is the same as 8 less than twice the larger.
5y = 2x - 8 rewritten as 2x - 5y = 8
Therefore we have
x - y = 16 which is 2x - 2y = 32 (i)
and 2x - 5y = 8 (ii)
(i) - (ii) gives:
2x - 2x - 2y -- 5y = 32 - 8
(-- is +)
3y = 24
y = 8
Substitute in (1): 2x - 16 = 32
2x = 48
x = 24
Therefore x=24, y=8.
24 is the larger, 8 is the smaller.
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