Clara spends her entire budget and consumes 5 units of x and 13 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 13 units of y, what is the largest number of units of x that she can afford?
A)10
B)5
C)12
D)14
E)There is not enough information to say.

Question

Quizplus · Accepted Answer

Initially, let the price of y be $P_y$ and the price of x be $P_x = 2P_y$. Clara's initial income is $I$. Her expenditure on y is $13P_y$ and on x is $5(2P_y) = 10P_y$, so her total expenditure (which equals her income) is $13P_y + 10P_y = 23P_y$. Therefore, $I = 23P_y$.When her income doubles and the price of y doubles, her new income is $2I = 2(23P_y) = 46P_y$, and the new price of y is $2P_y$. If she buys 13 units of y at the new price, her expenditure on y is $13(2P_y) = 26P_y$.The remaining income for buying x is $46P_y - 26P_y = 20P_y$. Since the price of x remains $2P_y$, the largest number of units of x she can afford is $20P_y / (2P_y) = 10$.

Clara Spends Her Entire Budget and Consumes 5 Units of X