Math 1324 test review

Question

A bar owner wants to purchase sets of red wine glasses and white wine glasses. He wants to have 200 total glasses at the bar. Each red wine glass costs $3 and each white wine glass costs $2.50. If he only has $570 to spend on the glasses, how many of each type will can he buy?

Answer 1

Here's what we know:

r + w = 200 (the bar owner want 200 red and white wine glasses in total)

3r + 2.5w = 570 (the cost of the wine glasses should equal up to $570)

Let's use substitution to solve this, and do so by isolating w in the first equation:

w = 200 - r

Place that value in the second equation:

3r + 2.5(200 - r) = 570

3r + 500 - 2.5r = 570

0.5r + 500 = 570

Subtract 500 from both sides:

.5r = 70

Divide by .5 (or multiply by 2):

r = 140

Now to find the white wine glasses:

w = 200 - 140

w = 60

check:

3 * 140 + 2.5 * 60 = 570

420 + 150 = 570

570 = 570