Madeleine allows herself $100 per month for purchasing coffee.The diagram below illustrates the choices available to her.
FIGURE 1- 3
-Refer to Figure 1- 3.Which of the following combinations of regular coffees and lattes is affordable over the one- month period,given Madeleine's budget?
A)15 lattes and 30 coffees
B)16 lattes and 16 coffees
C)20 lattes and 80 coffees
D)4 lattes and 66 coffees
E)8 lattes and 50 coffees

Question

Madeleine allows herself $100 per month for purchasing coffee.The diagram below illustrates the choices available to her.
  FIGURE 1- 3
-Refer to Figure 1- 3.Which of the following combinations of regular coffees and lattes is affordable over the one- month period,given Madeleine's budget?
A)15 lattes and 30 coffees 
B)16 lattes and 16 coffees 
C)20 lattes and 80 coffees 
D)4 lattes and 66 coffees 
E)8 lattes and 50 coffees

Quizplus · Accepted Answer

Madeleine's budget is $100 per month. Each regular coffee costs $1.50 and each latte costs $3.50. Let x be the number of regular coffees and y be the number of lattes that Madeleine buys in a month. Then, the total amount spent on coffee is 1.5x + 3.5y, and this must be less than or equal to $100.
Using this inequality, we can determine which choices are affordable:
A) 15 lattes and 30 coffees: 1.5(30) + 3.5(15) = 97.5 (affordable)
B) 16 lattes and 16 coffees: 1.5(16) + 3.5(16) = 80 (affordable)
C) 20 lattes and 80 coffees: 1.5(80) + 3.5(20) = 170 (not affordable)
D) 4 lattes and 66 coffees: 1.5(66) + 3.5(4) = 106 (not affordable)
E) 8 lattes and 50 coffees: 1.5(50) + 3.5(8) = 83 (affordable)
Therefore, the only affordable option is choice B: 16 lattes and 16 coffees. This combination costs $80, which is within Madeleine's budget of $100 per month.

Madeleine Allows Herself $100 Per Month for Purchasing Coffee