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Kayden and his children went into a grocery store where they sell apples for $0.75 each and mangos for $2 each. Kayden has $20 to spend and must buy a minimum of 16 apples and mangos altogether. Also, he must buy no less than 16 apples. If x represents the number of apples purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.

User Sreejesh
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If x represents the number of apples purchased and y represents the number of mangos we can set up the following:

Kayden has $20, so can spend up to this amount:

  • 0.75x + 2y ≤ 20

He must buy a minimum of 16 apples and mangos altogether:

  • x + y ≥ 16

Also, he must buy no less than 16 apples:

  • x ≥ 16

We also need to consider y can't be negative, hence add one more inequality:

  • y ≥ 0

Plot all four inequalities and see what is the zone of intersection.

The solution is the set of whole coordinates for x and y within the triangle with vertices at (16, 0), (16, 4) and (26.67, 0).

One possible solution is (20, 2) another one (24, 1).

See attached.

Kayden and his children went into a grocery store where they sell apples for $0.75 each-example-1
User Saeed Rohani
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