Paul mixes nuts worth $1.20 per pound with oats worth $1.70 per pound to get
40 pounds of trail mix worth
$1.35 per pound. How many pounds of nuts and how many pounds of oats did he use?
see the related questions below, or the mixture problems posted after this one.
To solve this problem, let's assume Paul used x pounds of nuts and y pounds of oats.
Given:
The cost of nuts per pound = $1.20
The cost of oats per pound = $1.70
The total weight of the trail mix = 40 pounds
The cost of the trail mix per pound = $1.35
We now set up two equations based on the information given:
Equation 1: x + y = 40 (since the total weight of the trail mix is 40 pounds)
Equation 2: (1.20x + 1.70y) / 40 = 1.35 (since the cost of the trail mix per pound is $1.35)
Now, let's solve the equations to find the values of x and y:
From Equation 1, we can rewrite it as x = 40 - y and substitute it into Equation 2:
(1.20(40 - y) + 1.70y) / 40 = 1.35
Expanding and simplifying:
(48 - 1.2y + 1.70y) / 40 = 1.35
(48 + 0.5y) / 40 = 1.35
Cross multiply:
(48 + 0.5y) = 1.35 * 40
48 + 0.5y = 54
Subtract 48 from both sides:
0.5y = 54 - 48
0.5y = 6
Divide both sides by 0.5:
y = 6 / 0.5
y = 12
Now substitute the value of y into Equation 1:
x + 12 = 40
x = 40 - 12
x = 28
Therefore, Paul used 28 pounds of nuts and 12 pounds of oats to make 40 pounds of trail mix.