Question

Joyce wants to mix granola and raisins together to make a snack for her class. Granola costs $2 per pound and raisins cost $4.50 per pound. Joyce is willing to spend $37.50 and wants to make 15 pounds of trail mix. Which system of equations could Joyce use to figure out how many pounds of granola (g) and raisins (r) she should buy?
A) 35 pounds
B) 36 pounds
C) 54 pounds
D) 72 pounds

Answer 1

The answer to the question is D

Answer 2

Answer:

System of equation is

g + r = 15  

2g + 4.50r = 37.50  

Joyce  needs to mix 3 pounds of raisins and 12 pounds of granola.

Step-by-step explanation:

Given : Joyce wants to mix granola and raisins together to make a snack for her class. Granola costs $2 per pound and raisins cost $4.50 per pound and Joyce is willing to spend $37.50 and wants to make 15 pounds of trail mix.

We have to write the system of equations could Joyce use to find the amount of  pounds of granola (g) and raisins (r) she should buy.

Consider  she buys g pounds of granola

and r pounds of  raisins.

then total amount of snacks  is 15 pounds

So , this can be written as g + r = 15  

Also, Cost of one pound of Granola = $2

So , cost of g  pounds of granola  is 2g

Cost of one pound of Raisins= $4.50

So , cost of r  pounds of Raisins  is 4,50r

She spend  $37.50 on mixture.

2g + 4.50r = 37.50  

Thus, we have system as

g + r = 15  .....(1)

2g + 4.50r = 37.50   ....(2)

Solving equation (1) and (2) , we have,

Using elimination method,  

Multiply (1) by 2

(1) ⇒ 2g + 2r = 30  ........(3)

Now subtract (3) and (2) , we get,

2g + 4.50r -(2g + 2r) = 37.50 - 30

4.50r - 2r  = 7.50

2.50 r = 7.50

r = 3

Put r = 3 in (1) , we get,

g + r = 15 ⇒ g = 15 - 3 = 12

Thus, Joyce  needs to mix 3 pounds of raisins and 12 pounds of granola.