Question

A parent is going school shopping for her children. She has $56.50 to spend on school supplies and wants to purchase at least 16 items. Composition notebooks cost $3.99 each and pencils cost $1.99 a box. Write a system of inequalities to show how many composition notebooks, x, and pencil boxes, y, the parent can afford to buy.

a) 3.99x + 1.99y ≥ 56.50, x + y ≥ 16
b) 3.99x + 1.99y ≤ 56.50, x + y ≥ 16
c) 3.99x + 1.99y ≥ 56.50, x + y ≤ 16
d) 3.99x + 1.99y ≤ 56.50, x + y ≤ 16

Answer 1

The correct system of inequalities for a parent shopping with $56.50 to buy at least 16 items, with notebooks at $3.99 and pencils at $1.99, is 3.99x + 1.99y ≤ 56.50 and x + y ≥ 16 (option b).

Step-by-step explanation:

The correct system of inequalities for the scenario where a parent is shopping for school supplies with $56.50 and wants to purchase at least 16 items, with composition notebooks costing $3.99 each and pencils costing $1.99 a box, is given by the inequalities:
3.99x + 1.99y ≤ 56.50, which represents that the total cost of x composition notebooks and y boxes of pencils should be less than or equal to $56.50. The second inequality is x + y ≥ 16, which indicates that the parent needs to buy at least 16 items in total.

Hence, the correct system of inequalities is option b: 3.99x + 1.99y ≤ 56.50, x + y ≥ 16.