Question

Fiona 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 Follies sold at least $300 worth of cupcakes and muffins and its expenses were no more than $100.
Let x be the number of cupcakes sold last Monday.
Which ordered pairs representing a combination of cupcakesand muffins could have been sold last Monday and make sense in the context of the situation.
Select each correct answer.
[] (32.5, 140)
[] (40, 80)
[] (60, 70)
[] (79, 42.5)
[] (80, 80)

Answer 1

Let x be the number of cupcakes sold and y be the number of muffins sold.

Income earned on x cupcakes and y muffins is 3x+2y.

And Expenses on x cupcakes and y muffins is 0.75x+0.5y.

Given that earned money on cup cakes and muffins is at least 300$.

That is 3x+2y ≥ 300

And also given that expenses are no more than 100$

That is 0.75x+0.5y ≤ 100

Now we have to find the ordered pairs among the given options satisfying above 2 inequalities.

a) 3x+2y = 3*32.5+ 2*140 = 377.5>300

  0.75x+0.5y = 0.75*32.5+0.5*140 = 94.375<100

Hence first pair is satisfying.

Like this we can conclude that (60,70) and (79,42.5) and (80,80) are also satisfying the above conditions.

Hence correct options are a,c,d and e.