Question

Five times the difference of twice a number and three,
decreased by the sum of the number and eight, equals 13.

Answer 1

The equation of this word problem is 5 (2x-3) - (x+8) = 13.

Step-by-step explanation:

Let the number be x

a) 5 times the difference of twice a number and 3

1. twice a number = 2x

2. difference of twice a number and 3 = 2x-3

3. 5 times the difference of twice a number and 3 = 5(2x-3)

b) Decreased by the sum of the number and eight

4. sum of number and eight = x + 8

5. a decreased by sum of number and eight = 5(2x-3) - (x+8)

c) Equals 13

6. 5(2x-3) - (x+8) = 13

Solve to find x

5 (2x-3) - (x+8) = 13

10x-15-x+8 = 13

10x-x-15+8 = 13

9x-7 = 13

9x = 13+7

9x = 20

x = $\frac{20}{9}$

Therefore, the equation of this word problem is 5 (2x-3) - (x+8) = 13.

Keyword: difference, equation

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