Solving Two Variable Algebraic Expressions

What is the value of a in the equation 3a + b = 54 when b = 9?

• 15

• 18

• 21

• 27

• 20

• 32

• 44

• 48

The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1m?

• 2x - 2.1 = 7.5

• 4.2 + y = 7.5

• y - 4.2 = 7.5

• 2.1 + 2x = 7.5

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made for a total cost of $43.92?

• x + y = 15.98

• x + y = 43.92

• 43.92x - 2.99y = 12.99

• 2.99x + 12.99y = 43.92

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation she could use to find the number of bottles she needs to sell to earn a total of $100.

1.25x + 1.49 = 100

What error did Barbara make in writing the equation?

• Barbara's equation did not consider the number of bottles of water.

• Barbara's equation did not consider the number of bottles of iced tea.

• Barbara's equation did not use the correct price for the bottles of iced tea.

• Barbara's equation did not use the correct total for her desired sales.

The town librarian bought a combination of new-release movies on DVD for $20 each and classic movies on DVD for $8. Let x represent the number of new-releases, and let y represent the number of classics. The librarian had a budget of $500 and wanted to purchase as many DVD's as possible. Which values for x and y would give her the highest number of total DVD's while still maintaining the budget?

• x = 8 and y = 45

• x = 10 and y = 22

• x = 18 and y = 22

• x = 18 and y = 18

• Malik did not multiply correctly in the final step.

• Malik added 240 to both sides of the equation in the fourth line of the work, which was not the correct thing to do.

• Malik substituted 60 for y instead of x in the second line of the work.

Chen is brining fruits and veggies to serve in an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruits. The food cost is modeled by the equation below, where v represents the cost of one pint of cut veggies, and f represents the cost of one pint of cut fruits. If the cost of each pint of cut fruits is $2.85, what is the cost of one pint of cut veggies (rounded to the nearest cent)?

Equation: 5v + 7f = 28.70

• $1.75

• $2.06

• $2.39

• $3.99

What is the value of y in the equation below when x = 3 ?

6.4x + 2.8y = 44.4

• y = 5

• y = 6

• y = 8

• y = 9

Which ordered pairs satisfy the equation? CHECK ALL THAT APPLY.

5x + 8y = 80

• (0, 10)

• (0, 16)

• (8, 5)

• (0, 0)

• (-16, 20)