Problem Solving

A company makes a profit of 6 percent on its first $1,000 of sales each day, and 5 percent on all sales in excess of $1,000 for that day. How many dollars in profit will the company make on a day when sales are S dollars if S is greater than 1,000?

A. 0.05S
B. 0.06S
C. 110
D. 10 + 0.05S
E. 60 + 0.05S

The OA is D.

We can just plug in some values to find out:

Say S = 1100
For the first 1000, profit is 6% i.e. $60
For the next 100, profit is 5% i.e. $5
Total profit is $65

Plug in 1100 in the options and you see that option D will give you 65.

Please, can anyone explain another way to solve this PS question? Thanks!

BTGmoderatorLU wrote:A company makes a profit of 6 percent on its first $1,000 of sales each day, and 5 percent on all sales in excess of $1,000 for that day. How many dollars in profit will the company make on a day when sales are S dollars if S is greater than 1,000?

A. 0.05S
B. 0.06S
C. 110
D. 10 + 0.05S
E. 60 + 0.05S

The OA is D.

Hello BTGmoderatorLU.

Let's see another way to solve it.

The sales of the company on a day are S > $1,000.

Then, for the first $1,000 the profit is equal to $$P_1=1,000\cdot6\%=1,000\cdot\frac{6}{100}=10\cdot6=60.$$ Thta is to say, for the first $1,000 the company makes a profit of $60.

Now, the amount of dollars in excess of $1,000 we can represent it by S-1,000. Therefore, the profit for the excess of $1,000 is equal to $$P_2=\left(S-1,000\right)\cdot5\%=\left(S-1,000\right)\cdot\frac{5}{100}=\left(S-1,000\right)\cdot\frac{1}{20}=\frac{1}{20}\cdot S-\frac{100}{2}=0.05\cdot S-50.$$ Finally, the company wil make in profit the following amount of dollars $$P_1+P_2=60+0.05\cdot S-50=10+0.05\cdot S$$ This implies thta the correct answer is the option D.

I hope it helps you.

Regards.