Question

Select the correct answer. A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel? A. $15 and $10 B. $13.50 and $7.50 C. $12 and $5.50 D. $10.50 and $3

Answer 1

Okay, let's represent the price of a bed sheet with 'b' and a towel with 't':

54b + 50t = 923

38b + 61t = 791.50

Now, if we subtract both sides by 54b (on the first equation), we get this:

50t = 923 - 54b

Divide both sides by 50:

t = 18.46 - 1.08b

Now that we know this, we can move on to the 2nd equation:

38b + 61t = 791.50

Input the variable 't':

38b + 61(18.46 - 1.08b) = 791.5

38b + 1126.06 - 65.88b = 791.5

38b - 65.88b = 791.5 - 1126.06

Simplify:

-27.88b = -334.56

Because both sides are negative, we can turn it into a positive:

27.88b = 334.56

b = 334.56/27.88

b = 12

Now that we know that b = 12, we can easily input it into any equation:

648 + 50t = 923

50t = 275

t = 5.5

One bed sheet costs $12 and one towel costs $5.50

Option C is the answer.