Question

A drama teacher has a budget of $120 to spend on materials to create costumes for a play. She can buy 1 square yard of white material for $8, while 1 square yard of blue material costs $10. Let x represent the number of square yards of white fabric purchased and y be the number of square yards of blue fabric. Then the inequality 8x+10y≤120 graphed below determines how many square yards of each type of fabric can be bought without exceeding the budget. If the teacher wants to buy 10 square yards of white fabric, what is the greatest whole number of square yards of blue fabric that she can buy without exceeding the budget?

Answer 1

Inequalities are used to relate unequal expressions

The greatest whole number of square yards the teacher can buy is 4

The inequality is given as:

$8x + 10y \le 120$

When the number of square yards of the white fabrics is 10.

It means that: x = 10

So, we have:

$8 \times 10 + 10y \le 120$

$80 + 10y \le 120$

Collect like terms

$10y \le 120 - 80$

$10y \le 40$

Divide both sides by 10

$y \le 4$

The above inequality means that:

The greatest whole number of square yards the teacher can buy is 4

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