Question

Maria spends her entire budget and consumes 5 units of x and 6 units of y. The price of x is twice the price of y. Her income doubles and the price of y doubles, but the price of x stays the same. If she continues to buy 6 units of y, what is the largest number of units of x that she can afford?

Answer 1

Maria can now afford 2.5 units of x.

Step-by-step explanation:

To find the largest number of units of x that Maria can afford, we need to compare the prices of x and y. Since the price of x is twice the price of y, Maria can buy 5 units of x and 6 units of y with her entire budget.

When Maria's income doubles and the price of y doubles, her budget constraint shifts. She continues to buy 6 units of y, so we need to calculate how many units of x she can now afford.

If the price of y doubles, Maria's budget for y is halved. This means she can only buy half the number of units of y compared to before. Since she continues to buy 6 units of y, she now has half the budget left for x compared to before.

Therefore, Maria can now afford 2.5 units of x.

Answer 2

10

Step-by-step explanation:

Let Maria's entire budget be B.

"Maria spends her entire budget and consumes 5 units of x and 6 units of y."

5x + 6y = B

x = 2y

5(2y) + 6y = B

10y + 6y = B

16y = B

B = 16y

"Her income doubles and the price of y doubles, but the price of x stays the same."

Her new budget is now 2B, or 32y, and the price of y doubles to 2y, so 6 units of y now cost 12y. Now the price of y equals the price of x.

2B - 12y = 2(16y) - 12y = 32y - 12y = 20y

Since the price of x and y are now the same, and are both 2y. Since she has 20y left after buying 6 units of y, she can by 20y/2y = 10 units of x.

Answer: 10