The school athletic director had a budget of $500 to purchase 164 items for the soccer team. She purchased vests for $2.50 each, soccer bal

Question

The school athletic director had a budget of $500 to purchase 164 items for the soccer team. She purchased vests for $2.50 each, soccer balls for $9.25 each, and cones for $0.75 each. She purchased 40 more cones than soccer balls.

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Eirian 4 years 2021-09-05T06:43:54+00:00 1 Answers 30 views 0

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  1. ngocdiep
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    2021-09-05T06:45:01+00:00
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    The question is incomplete:

    The school athletic director had a budget of $500 to purchase 164 items for the soccer team. She purchased vests for $2.50 each, soccer balls for $9.25 each, and cones for $0.75 each. She purchased 40 more cones than soccer balls. How many of each item can she purchase?

    Answer:

    She can purchase 60 vests, 32 soccer balls and 72 cones.

    Step-by-step explanation:

    You can write the following equations:

    x+y+z=164 (1)

    2.50x+9.25y+0.75z=500 (2)

    y=z-40 (3), where:

    x is the amount of vests

    y is the amount of soccer balls

    z is the amount of cones

    First, you have to replace (3) in (1) and (2):

    x+z-40+z=164

    x+2z=204 (4)

    2.50x+9.25(z-40)+0.75z=500

    2.50x+9.25z-370+0.75z=500

    2.50x+10z=870 (5)

    Now, you have two equations:

    x+2z=204 (4)

    2.50x+10z=870 (5)

    Then, you have to isolate x in (4)

    x=204-2z (6)

    After this, you can replace (6) in (5):

    2.50(204-2z)+10z=870

    510-5z+10z=870

    5z=870-510

    5z=360

    z=360/5

    z=72

    Next, you can replace the value of z in (6):

    x=204-2z

    x=204-2(72)

    x=204-144

    x=60

    Finally, you can replace the value z in (3):

    y=z-40

    y=72-40

    y=32

    According to this, the answer is that she can purchase 60 vests, 32 soccer balls and 72 cones.

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