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.
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.