Question

A store manager calculates his store's monthly utility expenses using two expense rates $r_1$ for the dollar cost per hour the store was open during the month and $r_2$ for the dollar cost per hour the store was not open during the month. During November, which has 30 days, the store was open 8 hours a day, except one day when it was open for 15 hours for a special sale. Which of the following expressions should the manager use to calculate the store's utility expenses, in dollars for November ?

• A. $247r_1+473r_2$
• B. $\left(247r_1\right)\left(473r_2\right)$
• C. $473r_1+247r_2$
• D. $\frac{473r_1}{247r_2}$

Answer 1

The correct option is A $247r_1+473r_2$

Step 1 : Underline the key words
A store manager calculates his store's monthly utility expenses using two expense rates $r_1$ for the dollar cost per hour the store was open during the month and $r_2$ for the dollar cost per hour the store was not open during the month. During November, which has 30 days, the store was open 8 hours a day, except one day when it was open for 15 hours for a special sale.

Step II Recognize the variable
Since, the store was open for 8 hours on 29 days and for 15 hours on remaining one day.
So the total number of hours the shop was open is 8(29) + 15 = 247 hours.
Therefore, the cost incurred by the shop for the number of hours it was open $=247r_1$
There are 720 hours in the 30 days of November. The number of hours the shops remain closed = 720 -247 = 473
Therefore, the cost incurred by the shop for the number of hours it was closed $=473r_2$
Therefore, the total expense $=247r_1+473r_2$

Hence, option A is correct.