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 sol

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?

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Tryphena 5 years 2021-07-27T10:17:29+00:00 1 Answers 22 views 0

Answers ( )

  1. thucuc
    0
    2021-07-27T10:19:08+00:00
    Reply

    Answer:

    x = 4

    y = 6

    z = 5

    Step-by-step 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

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