Equations and Word Problems

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

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What is the y-coordinate to the system of equations below? -4x + y = 4 4x - 3y = 12

• y=3

• y=8

• y=-3

• y=-8

What is the value of y in the solution to this system of equations? 6y + x = -59 x = -2y + 9

• 8.5

• -17

• 43

• -12.5

A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses.

How many courses worth 3 credits did the student complete?

• 13

• 5

• 20

• 39

What is the value of x in the solution to this system of equations? 3x - 5y = 22 y = −5x + 32

• -6.5

• 0.5

• 6.5

• -0.5

What is the solution to this system of equations?

8x − 4y = −16

3x + 15y = −6

• (2,0)

• (0,-2)

• (-2,0)

• (0,2)

Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

• The first customer paid $12 for 14 postcards and 5 large envelopes.

• The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

• $1.42

• $0.35

• $1.15

• $0.63

What is the x-value of the solution to this system of equations? x = 2y − 4 7x + 5y = −66

• -2

• -19/7

• -8

• -62/19

The larger of two numbers is two more than five times the smaller number. If the sum of the two numbers is 80, what is the SMALLER number?