SOLUTION: Please help to solve this problem: the larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number. thank you Rick

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Question 216081: Please help to solve this problem:
the larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number.
thank you
Rick
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Please help to solve this problem:

The larger of 2 numbers is 20 more than the smaller. 4 times the larger is 70 more than 5 times the smaller, find the number.

thank you
Rick

Step 1. Let x be the smaller number and let x+20 be the larger number.

Step 2. Let 4(x+20) be four times the larger.

Step 3. Let 5x be five times the smaller.

Step 4. Then 4%28x%2B20%29=+5x%2B70 since 4 times the larger is 70 more than 5 times the smaller.

Step 5. The following steps will solve the equation in Step 4.

4%28x%2B20%29=+5x%2B70

4x%2B80=5x%2B70

Subtract 4x+70 from both sides of the equation to get x-terms on the right side and numbers on the left side of the equation.

4x%2B80-4x-70=5x%2B70-4x-70

10=x and x%2B20=30

Check if 4%28x%2B20%29=+5x%2B70 or 4%2A30=5%2A10%2B70 which is a true statement.

Step 6. ANSWER. The numbers are 10 and 32.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J