Problem Solving

Princeton Review

The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A. \(9y - \frac{xy}{100}\)

B. \(9y + xy\)

C. \(9y - xy\)

D. \(\frac{9y-xy}{9}\)

E. \(\frac{y-xy}{6}\)

OA A

Question: Which of the following represents food purchases in dollar for the first 9 months of a year?

The average American, spent $y on food per month,
In January, Food purchases are x% lower than other months.
$$x\ \%\ y=\frac{x}{100}\cdot\frac{y}{1}=\frac{xy}{100}$$
$$Then,\ January\ food\ purchase=y-\frac{xy}{100}$$
So, food purchase for the first 9 months of a year,
$$January;\ y-\frac{xy}{100}$$ $$other\ 8\ months=y$$ $$Total\ \cos t=y-\frac{xy}{100}+\left(8y\right)$$