Question

Translate to a system of equations and solve:

Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her \(6 per pound. Peanuts are \)4 per pound and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?

Short answer

The number of pounds of peanuts and cashews are 3 and 2 respectively.

Step-by-step solution

Step 1. Given Information 

The given data is that Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound and cashews are $9 per pound.

Step 2. Calculation  

Let the number of peanuts be x and the number of cashews be y.

Mixture cost is $6 per pound and total number of units are 5 units that is $x+y=5--\left(1\right)$

Total value of mixture can be expressed as role="math" localid="1647679360198" $4x+9y=5\times 6--\left(2\right)$

Multiply equation (1) with number 4 and write the revised equation,

$$\begin{gathered} 4(x+y)=4\left(5\right) \\ 4x+4y=20--\left(3\right) \end{gathered}$$

Solve equation (2) and equation (3) by subtracting (3) from equation (2),

$$\begin{gathered} 4x+9y-4x-4y=30-20 \\ 5y=10 \\ y=2 \end{gathered}$$

Substitute the value of y in equation (1) to find the value of x.

$$\begin{gathered} x+2=5 \\ x=5-2 \\ x=3 \end{gathered}$$