Translating Words to Equations

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Show your work for each problem.

1.
Which equation represents "a number increased by 5 equals 12"?
1. a) $x = 5 + 12$
2. b) $5x = 12$
3. c) $x - 5 = 12$
4. d) $x + 5 = 12$
2.
What does "the product of 4 and a number" translate to?
1. a) $4x$
2. b) $\frac{4}{x}$
3. c) $4 - x$
4. d) $4 + x$
3.
Translate "5 less than $x$ " into an algebraic expression.
4.
Translate "the sum of $x$ and 8" into an algebraic expression.
5.
What operation does the word "quotient" indicate?
1. a)Division
2. b)Addition
3. c)Multiplication
4. d)Subtraction
6.
Translate "twice a number, decreased by 7" into an algebraic expression.
7.
Which equation represents "three times the sum of a number and 4 equals 21"?
1. a) $4(x + 3) = 21$
2. b) $3(x + 4) = 21$
3. c) $3x + 4 = 21$
4. d) $3 + x + 4 = 21$
8.
Translate and solve: "A number multiplied by 4, then increased by 6, equals 30."
9.
Write an equation for: "8 more than triple a number is 29." Then solve.
10.
A shirt costs 12 dollars more than a hat. The shirt costs 35 dollars. Let $h$ = the hat's cost. Write an equation that says the shirt costs 35 dollars.
11.
Maria's age is 3 years less than twice her sister's age. Maria is 15. How old is her sister?
12.
Which equation represents "the difference between a number and 7, divided by 2, equals 5"?
1. a) $\frac{x - 7}{2} = 5$
2. b) $\frac{7 - x}{2} = 5$
3. c) $x - \frac{7}{2} = 5$
4. d) $\frac{x}{2} - 7 = 5$
13.
A regular concert ticket costs 5 dollars more than half the price of a VIP ticket. The regular ticket costs 35 dollars. What is the VIP ticket price?
14.
The perimeter of a rectangle is 48 cm. The length is 6 cm more than the width. Find the width.
15.
You earn 15 dollars per hour plus a 25 dollar bonus. Write an equation for total earnings ( $E$ ) in terms of hours worked ( $h$ ).
16.
The sum of three consecutive integers is 72. Find the smallest integer.