Algebraic Equations

Write an equation for the word sentence:
The sum of a number and 4.5 is 8.2.

• 8.2=4.5n

• n+4.5=8.2

• 8.2n=4.5

• n-4.5=8.2

Determine whether the given value of the variable is a solution of the equation.
x - 24 = 58;  x = 82

• yes

• no

Determine whether the given value of the variable is a solution of the equation.
⅓c = ⅜; c = ¾

• no

• yes

Solve the equation:
a + 2.4 = 7.8

• a = 10.2

• a = 5.4

• a = 17.76

• a = 3.25

Solve the equation:
b - ¼ = 3 ½

• b = 3 ¼

• b = 14

• b = ⅞

• b = 3 ¾

Solve the equation:
⅓s = ⅕

• s = ⅕

• s = ⅗

• s = 5/3

• s = 2/15

Solve the equation:
w ÷ 7 = 0.3

• w = 0.043

• w = 7.3

• w = 2.1

• w = .3/7

A stadium has a total of 18,000 seats. Of these, 7,500 are field seats, and the rest are grandstand seats. Which equation could be used to find the number of grandstand seats s?

• s + 7,500 = 18,000

• s - 7,500 = 18,000

• s + 18,000 = 7,500

• s - 18,000 = 7,500

Aaron wants to buy a bicycle that costs $128. So far, he has saved $56. The equation
a + 56 = 128 can be used to find the amount a in dollars that Aaron still needs to save. What is the solution of the equation?

• a=64

• a=72

• a=132

• a=184

Ms. McNeil buys 2.4 gallons of gasoline.
The total cost is $7.56. The equation
2.4p = 7.56 can be used to find the price p in dollars of the one gallon of gasoline. What is the price of one gallon of gasoline?

• $1.81

• $2.40

• $3.15

• $5.16