Warm Up Sytems 4.6

Jimin ordered 20 total items consisting of pizza and sodas.  A pizza is $10, a soda is $2, and he spent a total of $72.  Which system models this scenario?

• 10P + 2S = 20
  P + S = 72

• P + S = 20
  2P + 10S = 72

• P + S = 20
  10P + 2S = 72

Answer explanation

The correct system is P + S = 20 (total items) and 10P + 2S = 72 (total cost). This reflects that Ben ordered 20 items of pizza (P) and soda (S) for a total of $72.

Namjoon rented a total of 12 movies and games.  A movie rents for $3 and a game rents for $4.50, for a total of $42.  Which system models this scenario?

• 3M + 4.50G = 42
  M + G = 12

• 3M + 4.50G = 12
  M + G = 42

• M + G = 12
  4.50M + 3G = 42

Answer explanation

The correct system is 3M + 4.50G = 42 (total cost) and M + G = 12 (total items). This represents the relationship between the number of movies (M) and games (G) rented by Uncle Freddy.

At a restaurant, Jimin finds that the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which system of equations represents this scenario? 

• 1t + 1m = 2.10

  2t + 3m = 5.15

• 1t + 1m = 5.15

  2t + 3m = 2.10

• 1t + 1m = 2.10

  1t + 3m = 5.15

• 2t + 1m = 2.10

  t + m = 5.15

Answer explanation

The first equation represents the cost of 1 taco (t) and 1 milk (m) totaling $2.10. The second equation represents the cost of 2 tacos and 3 milks totaling $5.15. Thus, the correct system is: 1t + 1m = 2.10 and 2t + 3m = 5.15.

Jennie finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Answer explanation

The equations represent the time taken for haircuts (x) and hair dyes (y). The first equation, 3x + 2y = 315, corresponds to 3 haircuts and 2 hair dyes, while the second, 2x + 4y = 450, corresponds to 2 haircuts and 4 hair dyes.

On Monday Jimin bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Answer explanation

The correct equations are 10c + 5d = 16.50 and 5c + 10d = 14.25, representing Joe's purchases on Monday and Tuesday respectively. These equations can be used to solve for the cost of coffee (c) and doughnuts (d).

1.  Jisoo bought 5 squash and 2 zucchini for $1.32. Namjoon bought 3 squash and 1 zucchini for $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75

• 5q + 2z = 1.32
  3q + 1z = 0.75

• q + z = 1.32
  q + z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

Answer explanation

The first equation represents the cost of 5 squash and 2 zucchini, while the second equation represents the cost of 3 squash and 1 zucchini. Thus, the correct system of equations is 5q + 2z = 1.32 and 3q + 1z = 0.75.

Jennie is trying to calculate the cost of a taxi ride using the formula y=mx+b, where y is the total cost, m is the rate per mile, x is the number of miles traveled, and b is the base fare. What does "m" represent in this equation?

• y-intercept

• slope

• macaroni

• nothing

Jimin is trying to understand the equation of a line, y=mx+b, while planning a garden. What does "b" represent in this equation?

• y-intercept

• slope

• macaroni

• nothing

Namjoon is designing a ramp for a skateboard park. He wants the ramp to follow a specific linear equation. Which equation represents the slope of the ramp he is planning?

• y = 3x + 2

• y = -2x + 3

• y = 2x + 3

• y = -3x + 2