Question

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.

Answer 1

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.