Question

Eight times a number increased by 9 exceeds 7 times the number by 15. Find the number.

Answer 1

turn it into math terms bit by bit. let x be "a number"

8 times a number is 8×x

increased by 9 is +9

7 times a number is 7×x

exceeds is minus

by 15 is =15

now we put it together.


`8 * x + 9 - 7 * x = 15`
solve

`8x + 9 - 7x = 15 \\ x + 9 = 15 \\ x = 6`

Answer 2

Remark

Reading the problem is more than 1/2 the trouble you will have with this question.

Start phrase by phrase. Let the number = x

The first phrase is 8 times a number so that is 8x

increased by 9. So that is 8x + 9

exceeds 7 times the number 8x + 9 - 7x

by 15 (translate that to equals 15)

Equation

8x + 9 - 7x = 15 Combine like terms.

x + 9 = 15 Subtract 9

x = 15 - 9

x = 6