SOLUTION: The sum of two numbers is 103. If four times the smaller number is subtracted from the larger number, the result is 8. Find the two numbers.

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Question 1119416: The sum of two numbers is 103. If four times the smaller number is subtracted from the larger number, the result is 8. Find the two numbers.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A formal algebraic solution as provided by the other tutor is of course valid; and something like that is of course required if the assignment requires an algebraic solution.

But solving problem like this informally, through logical reasoning and a little mental arithmetic, can be excellent exercise for the brain.

(1) The given information says that 8 remains after you subtract 4 times the smaller number from the larger.
(2) So subtract 8 from the larger number to get a "new" larger number; now when 4 times the smaller is subtracted from the new larger, the result is 0.
(3) That means the new larger number is exactly 4 times the smaller number; and that means the new sum is 5 times the smaller number.
(4) The new sum is 103-8 = 95; that means the smaller number is 95/5 = 19.
(5) Then the "new" larger number is 19*4 = 76; and so the original larger number is 76+8 = 84.