Translating Equations and Word Problems

Don earns $1400 a week for working 40 hours and an additional $17.50 an hour for each hour over 40. Last week, Don made $1452.50. How many hours over 40 did he work?

Translate the following: Fifteen plus the difference of twice a number and three is forty-five.

• 15 + 2x - 3 = 45

• 15 + (2x - 3) = 45

• (15 + 2x) + 3 = 45

• 15 (2x + 3) = 45

Five times the sum of x and 5 is 8 less than twice x. Solve for x.

Nine more than the quotient of a number and three is negative twenty-four. Solve for the variable.

Translate: ten more than a number is 52.

• x + 10 = 52

• 10 + x = 52

• 10x = 52

• x/10 = 52

Translate: eight less than a number is 24.

• 8 + x = 24

• x - 8 = 24

• 8 - x = 24

• 8x = 24

Translate: Three times a number decreased by 12 is 9.

• 12x - 3 = 9

• 9x - 3 = 12

• 3x - 12 = 9

• 3x - 9 = 12

Translate: ten more than four times a number is 30.

• 10 + 4x = 30

• 10x + 4 = 30

• 4x + 10 = 30

• 4(x +10) = 30

Dan's weekly budget is $125. He has already spent $50 on gas. How much money does he have left to spend?

Write an equation to represent this situation, using x to represent how much money he has left to spend.

• 50x = 125

• x/50 = 125

• x - 50 = 125

• x + 50 = 125

Tom had his birthday party at the movies. It cost $27 for pizza and $8.50 per friend for the movie tickets. How many friends did Tom have at the party if he spent $78? Write an equation to represent this situation. Use f to represent how many friends Tom has at the part.

• 8.50(f + 27) = 78

• 27f + 8.50 = 78

• 8.50f + 27 = 78

• 78 - 8.50f = 27