Questions: Paul mixes nuts worth 1.25 per pound with oats worth 1.70 per pound to get 27 pounds of trail mix worth 1.60 per pound. How many pounds of nuts and how many pounds of oats did he use? Paul used pounds of nuts and pounds of oats.

Paul mixes nuts worth 1.25 per pound with oats worth 1.70 per pound to get 27 pounds of trail mix worth 1.60 per pound. How many pounds of nuts and how many pounds of oats did he use?

Paul used pounds of nuts and pounds of oats.

Transcript text: Paul mixes nuts worth $\$ 1.25$ per pound with oats worth $\$ 1.70$ per pound to get 27 pounds of trail mix worth $\$ 1.60$ per pound. How many pounds of nuts and how many pounds of oats did he use? Paul used $\square$ pounds of nuts and $\square$ pounds of oats. Question Help:

Solution

Solution Steps

To solve this problem, we need to set up a system of equations based on the given information. Let $ x $ be the pounds of nuts and $ y $ be the pounds of oats. We have two equations: one for the total weight and one for the total cost. The total weight equation is $ x + y = 27 $. The total cost equation is $ 1.25x + 1.70y = 1.60 \times 27 $. We can solve this system of equations to find the values of $ x $ and $ y $.

Step 1: Set Up the Equations

We are given that Paul mixes nuts worth \$1.25 per pound with oats worth \$1.70 per pound to create 27 pounds of trail mix worth \$1.60 per pound. Let $ x $ be the pounds of nuts and $ y $ be the pounds of oats. We can set up the following system of equations:

Total weight equation: \[ x + y = 27 \]
Total cost equation: \[ 1.25x + 1.70y = 1.60 \times 27 \]

Step 2: Solve the Equations

Substitute the total cost equation with the calculated total cost: \[ 1.25x + 1.70y = 43.2 \]

We solve the system of equations: \[ \begin{align_} x + y &= 27 \\ 1.25x + 1.70y &= 43.2 \end{align_} \]

Step 3: Calculate the Values of $ x $ and $ y $

Solving the system of equations, we find: \[ x = 6, \quad y = 21 \]