SOLUTION: The sum of two numbers is 68. Five times the smaller number is 16 more than the larger. Find the two numbers.

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Question 1155830: The sum of two numbers is 68. Five times the smaller number is 16 more than the larger. Find the two numbers.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy
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system%28x%2By=68%2C5x=16%2By%29

5x=16%2B%2868-x%29
6x=16%2B68
6x=84
highlight%28x=14%29
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highlight%28y=54%29


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x and 68-x, the two numbers

cross%285%2868-x%29=16%2Bx%29
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cross%285%2A68-5x=x%2B16%29
cross%285%2A68-16=6x%29
x=cross%28%285%2A58-16%29%2F6%29

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system%28cross%2845%262%2F3%2Cand%2C22%261%2F3%29%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 68. Five times the smaller number is 16 more than the larger. Find the two numbers.
The WRONG ANSWER by the other person is a PRIME example of the importance of not only setting up the correct equation, but also setting up the EASIEST/LEAST

COMPLEX one. It also proves that the simplest equation with the SMALLEST numbers almost always assure, not only the correct answer but the easiest calculations.

Having said that, the following is one of, if not the EASIEST method, with which to solve this SIMPLE problem.

Let the smaller number be S

Then the larger is: 68 - S

Based on other "givens," we get the following equation: 5S = 68 - S + 16

Now, can an equation be any SIMPLER to solve?

HINT: If you don't know by now, the correct numbers are NOT cross%28matrix%281%2C3%2C+22%261%2F3%2C+and%2C+45%262%2F3%29%29

JOB WELL-DONE, tutor @JOSGARITHMETIC!