One number is five times another. If 18 is subtracted from the larger,

Question

the remainder will be three times the smaller. Find the number.

Answer 1

Let one number(smaller) be x.

Therefore the other number(larger) is 5x.

If 18 is subtracted from larger then the remainder is three times the smaller.

5x - 18 = 3x

Subtract 3x  from each side.

Apply Subtraction Property: If a = b then a - c = b - c.

5x - 18 - 3x = 3x - 3x

Apply Commutative Law of Addition: a + b = b + a.

5x - 3x - 18 = 3x - 3x

2x - 18 = 3x - 3x

Apply Additive Inverse Property: a + (-a) = 0.

2x - 18 = 0

Add 18 to each side.

Apply Addition Property: If a = b then a + c = b + c.

2x - 18 + 18 = 0 + 18

Apply Additive Inverse Property: -a + a = 0.

2x + 0 = 0 + 18

Apply Additive Identity Property: a + 0 = a.

2x = 18

Divide each side by 2.

Apply Division Property: If a = b then a/c = b/c.

2x / 2 = 18 / 2

Cancel common terms.

x = 9

Therefore smaller number = 9.

Larger number = 5x = 5(9) = 45.