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.
g+Response area=15
2Response area+4.5r=Response area
Using the given information, we can set up a system of equations:
g + r = 15 (since Joyce wants to make 15 pounds of trail mix)
2g + 4.5r = 37.5 (since Joyce wants to spend $37.50)
We can use the first equation to solve for g in terms of r:
g + r = 15
g = 15 - r
Then we can substitute this expression for g into the second equation and solve for r:
2g + 4.5r = 37.5
2(15-r) + 4.5r = 37.5
30 - 2r + 4.5r = 37.5
2.5r = 7.5
r = 3
Now that we know r = 3, we can use the first equation to solve for g:
g + r = 15
g + 3 = 15
g = 12
So Joyce needs 12 pounds of granola and 3 pounds of raisins to make 15 pounds of trail mix for her class. She will spend $24 on granola (12 pounds x $2 per pound) and $13.50 on raisins (3 pounds x $4.50 per pound), which adds up to exactly $37.50.