Question

The dishes have been sorted into cups and plates. The number of plates is four less than two times the

number of cups. The dishes are 60% plates. How many cups are there?

Answer 1

Explanation:

Let x be the number of cups and y be the number of plates. If we have 2 unknowns we need 2 equations, so let's find them.

We are told that the number of plates, y, is 4 less than twice the number of cups, so

y = 2x - 4

That's the first equation. We are also told then that the plates, y, are 60% of the total dishes. The dishes are cups and plates, so the dishes are x + y. If 60% of that is plates, and plates is y, then

y = .6(x + y)

That's the second equation. Sub the first into the second to get:

2x - 4 = .6(x + 2x - 4) and

2x - 4 = .6(3x - 4) and

2x - 4 = 1.8x - 2.4 and

.2x = 1.6 so

x = 8

There are 8 cups