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+___=15
2___+4.5r=____
g+ r = 15 (since she wants to make 15 pounds in total)
2g + 4.5r = 37.5 (since she is willing to spend $37.50)
We can use the first equation to solve for one of the variables in terms of the other. Let's solve for g:
g + r = 15
g = 15 - r
Now we can substitute this expression for g in the second equation:
2g + 4.5r = 37.5
2(15-r) + 4.5r = 37.5
30 - 2r + 4.5r = 37.5
2.5r = 7.5
r = 3
So Joyce should mix 12 pounds of granola and 3 pounds of raisins to make her trail mix. (12 + 3 = 15, and 2(12) + 4.5(3) = 37.5)