Question

daniel and his mom are working together to paint his bedroom. the paint store is currently offering the following sales.
item\tsale price
matte paint\t4 pints for $7.56
glossy paint\t2 gallons for $26.16
paint brushes\t4 for $18
calculate the unit rate of these items, and use that information to select all of the following statements that are correct. if necessary, round to the nearest penny.
a. daniel will spend $21.68 on matte paint if he buys 1\frac{1}{2} gallons.

b. daniel will spend $19.62 on glossy paint if he buys 6 quarts.

c. daniels total cost will be $24.12 if he buys 2 paint brushes and 1 gallon of matte paint.

d. daniel can buy 13 pints of glossy paint for $20.

Explanation:

Step1: Calculate matte paint unit rate

1 gallon = 8 pints, so 4 pints = 0.5 gallon. Unit rate: $\frac{7.56}{0.5} = 15.12$ dollars/gallon.

Step2: Calculate glossy paint unit rate

Unit rate: $\frac{26.16}{2} = 13.08$ dollars/gallon. 1 gallon = 4 quarts, so 1 quart = $13.08/4 = 3.27$ dollars.

Step3: Calculate paint brush unit rate

Unit rate: $\frac{18}{4} = 4.5$ dollars/brush.

Step4: Check statement A

$1\frac{1}{2}$ gallons = 1.5 gallons. Cost: $15.12×1.5 = 22.68$ dollars (not 21.68). A is wrong.

Step5: Check statement B

6 quarts = 1.5 gallons. Cost: $13.08×1.5 = 19.62$ dollars. B is correct.

Step6: Check statement C

2 brushes cost: $4.5×2 = 9$. 1 gallon matte paint cost: 15.12. Total: $9 + 15.12 = 24.12$ dollars. C is correct.

Step7: Check statement D

13 pints = 1.625 gallons. Cost: $13.08×1.625 ≈ 21.26$ dollars (over 20). D is wrong.

Answer:

B. Daniel will spend $19.62 on glossy paint if he buys 6 quarts, C. Daniel's total cost will be $24.12 if he buys 2 paint brushes and 1 gallon of matte paint.