if you could exactly afford either 2 units of x and 11 units of y, or 4 units of x and 7 units of y, then if you spent all of your income on y, how many units of y could you buy?
A)19
B)15
C)11
D)6
E)None of the above.

Question

Quizplus · Accepted Answer

We can set up a system of equations to solve for the cost of one unit of x and y:

2x + 11y = income
4x + 7y = income

Simplifying, we get:

2x + 11y = 4x + 7y
4y = 2x
y = 0.5x

So one unit of y costs half as much as one unit of x. Since we are spending all of our income on y, we want to maximize the number of units of y we can buy. If we buy 2 units of x and 11 units of y, we will have spent the same amount as if we had bought 4 units of x and 7 units of y. But since y is cheaper than x, we can buy more units of y by choosing the option with more units of y. Therefore, we would choose the second option of 4 units of x and 7 units of y, and we could buy 7 x 0.5 = 3.5 units of x. Rounded down, we can buy 15 units of y.

If You Could Exactly Afford Either 2 Units of X