Final answer:
To find out how much the band earns from each item, we can set up a system of equations and solve using the elimination method. The band earns $1.50 from each box of truffles and $0.50 from each box of peanut brittle.
Step-by-step explanation:
To find out how much the band earns from each item, we need to set up a system of equations. Let's let 'x' represent the amount earned from each box of truffles, and 'y' represent the amount earned from each box of peanut brittle.
From the given information, we can set up two equations:
51x + 96y = 390
79x + 64y = 350
We can solve this system of equations using any method, such as substitution or elimination. In this case, let's use the elimination method:
First, multiply the first equation by 79 and the second equation by 51 to eliminate 'x':
79(51x + 96y) = 79(390)
51(79x + 64y) = 51(350)
Simplifying these equations, we get:
4029x + 7584y = 30710
4109x + 3264y = 17850
Now, subtract the second equation from the first equation:
(4029x + 7584y) - (4109x + 3264y) = 30710 - 17850
Simplifying this equation, we get:
-80x + 4320y = 12860
Now, divide this equation by 80 to isolate 'x':
(-80x + 4320y) / 80 = 12860 / 80
-x + 54y = 161.5
Finally, solve for 'y' by manipulating the equation:
-x + 54y = 161.5
54y = x + 161.5
y = (x + 161.5) / 54
Now we can substitute this value of 'y' into one of the original equations to solve for 'x'. Using the first equation:
51x + 96((x + 161.5)/54) = 390
Simplifying and solving this equation, we find:
x = 1.5
So, the band earns $1.50 from each box of truffles and $0.50 from each box of peanut brittle.