SOLUTION: The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.

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Question 216536: The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.

Step 1. Let x be the first number and 92-x be the second number.

Step 2. Let x%2F5 be one-fifth of the first number

Step 3. Let %2892-x%29%2F2 be one half of the second number.

Step 4. Then, x%2F5%2B%2892-x%29%2F2=34 since the first number added to one half of the second number is 34.

Step 5. Solving yields the following steps.

Multiply 10 to both sides of the equation

10%2Ax%2F5%2B10%2A%2892-x%29%2F2=10%2A34

2x%2B5%2A%2892-x%29=340

460-3x=340

Add 3x-340 to both sides of the equation

460-3x%2B3x-340=340%2B3x-340

120=3x

Divide 3 to both sides of the equation

120%2F3=3x%2F3

x=40 and 92-x=52

Check...40%2F5%2B52%2F2=8%2B26=34...which is a true statement

Step 6. ANSWER: The numbers are 40 and 52.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J