Question

The local internet company charges $28 per hour during the day and $9.50 per hour at night. Esther paid $552 for 25 hours of use. The system of equations that represents this scenario is shown below, where d is the number of daytime hours and n is the number of nighttime hours. How many daytime hours and nighttime hours was Esther charged for?

28d+9.50n=552
d+25

a. 21 daytime hours and 4 nighttime hours
b. 8 daytime hours and 7 nighttime hours
c. 17 daytime hours and 8 nighttime hours
d. 12 daytime hours and 13 nighttime hours​

Answer 1

Explanation:

The given system of equations is:

28d + 9.5n = 552

d + n = 25

We can solve for one of the variables in the first equation and substitute that value into the second equation. Let's solve for d:

28d + 9.5n = 552

d = (552 - 9.5n) / 28

Now we can substitute this expression for d into the second equation:

d + n = 25

(552 - 9.5n) / 28 + n = 25

552 - 9.5n + 28n = 700

18.5n = 700 - 552

18.5n = 148

n = 8

So, we have found that n = 8, which represents the number of nighttime hours. To find the number of daytime hours, we can use the value of n and the first equation:

28d + 9.5n = 552

28d + 9.5 * 8 = 552

28d + 76 = 552

28d = 476

d = 17

Therefore, Esther was charged for 17 daytime hours and 8 nighttime hours, so the answer is (c) 17 daytime hours and 8 nighttime hours.