Question

Fiona's Follies is a small bakery that sells cupcakes and muffins. A cupcake sells for $3 and a muffin sells for $2. When all related business expenses are included, a cupcake costs $0.75 to prepare and a muffin costs $0.50 to prepare. Last Monday, Fiona's Follies sold at least $300 worth of cupcakes and muffins and its expenses were no more than $100. At most 80 cupcakes were sold. Let x be the number of cupcakes sold last Monday and y be the number of muffins sold last Monday. Which ordered pairs representing a combination of cupcakes and muffins could have been sold last Monday and make sense in the context of the situation? Select each correct answer. (80,80) (79,42.5) (40,80) (60,70) (32.5,140)

Answer 1

(60,70) And (80,80) will be the correct answers

:)

Answer 2

(80,80), (79,42.5) , (60,70) and (32.5, 140)

Explanation:

x: the number of cupcakes sold

y: number of muffins sold

Revenue: 3x + 2y

Expenses: 0.75x + 0.5y

Last Monday, the situation was:

3x + 2y ≥ 300

0.75x + 0.5y ≤ 100

x ≤ 80

Replacing (80,80) into the equations we get:

3(80) + 2(80) = 400 ≥ 300

0.75(80) + 0.5(80) = 100 ≤ 100

80 ≤ 80

which satisfies all equations.

Replacing (79,42.5) into the equations we get:

3(79) + 2(42.5) = 322 ≥ 300

0.75(79) + 0.5(42.5) = 80.5 ≤ 100

79 ≤ 80

which satisfies all equations.

Replacing (40,80) into the equations we get:

3(40) + 2(80) = 280

0.75(40) + 0.5(80) = 70 ≤ 100

40 ≤ 80

which doesn't satisfy first equation

Replacing (60,70) into the equations we get:

3(60) + 2(70) = 320 ≥ 300

0.75(60) + 0.5(70) = 80 ≤ 100

60 ≤ 80

which satisfies all equations.

Replacing (32.5, 140) into the equations we get:

3(32.5) + 2(140) = 377.5 ≥ 300

0.75(32.5) + 0.5(140) = 94.37500 ≤ 100

32.5 ≤ 80

which satisfies all equations.