Question

Translate the following verbal statement into an algebraic equation and then solve:

Use xx for your variable.

The sum of three times a number and six is nine more than the number.

Use xx for your variable.

The sum of four times a number and seven is ten.

Use xx for your variable.

The sum of three times a number and six is nine more than the number.

Equation

Translate the following verbal statement into an algebraic equation and then solve:

Use xx for your variable.

The sum of four times a number and seven is ten.

Answer 1

Answer: (1) Number is 3/2 OR 1.5 (2) Number is 3/4 OR 0.75

Explanation:

(1) Let the number is x. Then according to the statement "The sum of three times a number and six is nine more than the number", it can be written as,

3x+6=x+9 ------------------------------------- (1)

This is the algebraic equation of the problem.

subtracting x from both sides

3x+6-x=x+9-x

2x+6=9

subtracting 6 from both sides

2x+6-6=9-6

2x=3

dividing by 2 on both sides

2x/2=3/2

x=3/2=1.5

So, the number is 3/2 OR 1.5

(2) Let the number is x. Then according to the statement "The sum of four times a number and seven is ten", it can be written as,

4x+7=10 ----------------------------------------------------- (2)

This is the algebraic equation of the problem.

subtracting 7 from both sides

4x+7-7=10-7

4x=3

dividing by 4 from both sides

4x/4=3/4

x=3/4=0.750

So, the numbe is 3/4 OR 0.750