The difference of a larger number and a smaller number is 18. Find both numbers if the smaller number is ten more than one fifth the larger number.

Question

The difference of a larger number and a smaller number is 18. Find both numbers if the smaller number is ten more than one fifth the larger number

Answer 1

Let L be your larger number and let S be your smaller number.

Now, translate the first sentence.

The difference (subtract) of a larger and smaller number is 18.

L - S = 18.

Translate the next sentence "the smaller number is (means =) ten more than (add) 1/5 of (means multiply) the larger number.

S = 10 + 1/5L

Take what S and plug into L - S = 18 so you only have one variable to deal with

L - (10 + 1/5L) = 18  If you don't put parenthesis you may make a mistake with the minus sign!

L - 10 - 1/5L = 18   Multiply the ENTIRE equation through by 5 to get rid of the fraction

5L - 50 - L = 90    Collect like terms

4L - 50 = 90  Add the 50 to both sides

4L = 140  divide both sides by 4

L = 35  YOU ARE NOT DONE!!!  Answer the question asked!

L - S = 18 

35 - S = 18

S = 17.

Answer:  The two numbers are 17 and 18. :)