Question

Tristan and his children went into a grocery store that sells bananas for $0.70 each and peaches for $2 each. Tristan has $20 to spend and must buy no less than 12 bananas and peaches altogether. If xx represents the number of bananas purchased and yy represents the number of peaches purchased, write and solve a system of inequalities graphically and determine one possible solution.
Inequality 1: yy
≥


Inequality 2: yy
≥


0
x
y
Answer
Attempt 1 out of 2

Tristan could buy
bananas and
peaches. Submit Answer

Answer 1

Let x = number of bananas and y = number of peaches.

Inequalities:
- At least 12 items: x + y ≥ 12 → y ≥ 12 − x.
- Cost at most $20: 0.70x + 2y ≤ 20 → y ≤ 10 − 0.35x.
(Also x ≥ 0, y ≥ 0.)

Graphically the feasible region is the set of points between the line y = 12 − x (above) and the line y = 10 − 0.35x (below). The two lines intersect at x ≈ 3.08, y ≈ 8.92, so integer solutions start at x = 4.

One possible integer solution: x = 4 bananas and y = 8 peaches.
Check: 4 + 8 = 12 items and 0.70(4) + 2(8) = 2.8 + 16 = $18.80 ≤ $20.