Question

One number is two less than seven times another number. If the sum of the numbers is 22, find the numbers.

Answer 1

Answer:

19 and 3

Step-by-step explanation:

Given

Let both numbers be a and b.

So:

$a + b = 22$ --- Their sum

$a = 7b-2$ --- 2 less than 7 of the other number

Required

Find both numbers

$a + b = 22$

$a = 7b-2$

Substitute 7b - 2 for a in the first equation

$7b - 2 + b = 22$

Collect like terms

$7b + b = 22 + 2$

$8b = 24$

Divide both sides by 8

$\frac{8b}{8} = \frac{24}{8}$

$b = \frac{24}{8}$

$b = 3$

Substitute 3 for b in $a = 7b-2$

$a = 7 * 3 - 2$

$a = 21 - 2$

$a = 19$

Hence, the numbers are 19 and 3