A bakery is buying flouer and sugar from its supplier. The supplier will deliver no more than 750 pounds in a shipment. Each boag of flour weight 50 pounds and each bag of sugar weight 20 pounds. The bakery wants to buy at least three times as many bags of sugar as bags of flour. If f represents the number of bags of flour and s represents the number of bags of flour and s represents the number of bags of sugar, where f and s are nonnegative integers, which of the following system of inequalities represents this situation ?

Options

A. `50 f + 60 s le 750`
B. `50f +20s le 750`
`f le 3s`
C. `50f + 20s le 750`
`3f le s`
D. `150 f + 20s le 750`
`3f le s`

Answer

C

Explanation

Gegin by translating the weight of the combined bags of flour and suger. The weight of each bag of flour times the number of bags of flourplus the weight of each bag of sugar times the number of bags of sugar-will yield the total. Thus, `50f +20s` will describe the weight for all the bags combined. Since the weight that the supplier can deliver is no more than 750 poinds, the inequality that describes this situation is `50f + 20y le 750.` Eliminate (A) and (D).
The question also specifies that the bakery needs to buy at least theree times as many bags of sugar as bags of flour. In other words, then number of bags of sugar must be equal to or greater than three times the number of bags of flour. This is represented by `s ge 3f,` whihc can be rewritten as `3f les.` (C ) is correct.