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3 April, 22:45

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?

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  1. 3 April, 23:04
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    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
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