Applied Math- Inequalities

Question

A fundraiser for a school sells hoodies and track pants. Hoodies sell for $60 and track pants sell for $40. The school wants to raise at least $2000.

1. a) Write an inequality that models the situation.
2. b) Give a combination of hoodies and track pants that satisfies the inequality.

Answer 1

Let H = number of hoodies to sell and P = number of pants to sell

a)

Since the hoodies are $60 each, the money raised by selling hoodies can be shown by

60*H

The pants are $40 each, so the money raised by selling pants can be shown by

40*P

The school wants to raise at least $2000, so the total raised by selling hoodies and pants must be equal to or greater than $2000. We can show that by:

60H + 40P ≥ 2000

b) Part b asks only for a combination that will make it true, not for an optimized combination or something like that. All you need to do is find some combination that when added together is greater than or equal to $2000

Examples:

0 hoodies and 50 pairs of pants

(60 * 0) + (40*50) ≥ 2000

34 hoodies and 0 pants

(60*34) + (40*0) ≥ 2000

1000 hoodies and 1000 pants

(60*1000) + (40*1000) ≥ 2000

As long as the total dollars is greater than or equal to $2000 it will satisfy part b