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Chapter 5: Q. 5.93 (page 652)

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

Expert verified

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

Step by step solution

01

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.

02

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--(1)

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

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

4(x+y)=4(5)4x+4y=20--(3)

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

4x+9y-4x-4y=30-205y=10y=2

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

x+2=5x=5-2x=3

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In the following exercises, translate to a system of inequalities and solve.

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