Question

5. A store sells bags of pecans for $3.00, bags of walnuts for $3.50, and bags of almonds for $4.00. One day, 15

bags of nuts were sold, and $53 was earned for the sales. Two more bags of walnuts were sold than pecans.
Write a system of equations to represent this situation, define your variables, and then solve the system using
substitution. How many bags of each type of nuts were sold?

Answer 1

x = 4

y = 6

z = 5

Explanation:

Let

bags of pecans = x

bags of walnuts = y

bags of almonds = z

x + y + z = 15

3x + 3.5y + 4z = 53

Two more bags of walnuts were sold than pecans.

Walnuts = x + 2

x + y + z = 15

3x + 3.5y + 4z = 53

x + x + 2 + z = 15

3x + 3.5(x+2) + 4z = 53

2x + z = 15 - 2

3x + 3.5x + 7 + 4z = 53

2x + z = 13 (1)

6.5x + 4z = 46 (2)

Multiply (1) by 4

8x + 4z = 52 (3)

6.5x + 4z = 46 (2)

Subtract (2) from (3)

8x - 6.5x = 52 - 46

1.5x = 6

Divide both sides by 1.5

x = 4 bags

y = x + 2

= 4 + 2

= 6

y = 6 bags

Substitute the value of x into (1)

2x + z = 13 (1)

2(4) + z = 13

8 + z = 13

z = 13 - 8

= 5

z = 5 bags

Check:

x + y + z = 15

4 + 6 + 5 = 15