Question

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

Option: C is the correct answer.

C.) $12 and $5.50

Explanation:

Let the cost of one bed sheet is: $ x

and cost of one towel is: $ y

Now, it is given that:

• A dormitory manager buys 38 bed sheets and 61 towels for $791.50.

i.e. the equation is written as:

38x+61y=791.50

• The manager get another 54 bed sheets and 50 towels for $923

i.e. the equation is written as:

54x+50y=923

Now, in order to find the value of x and y we graph the system of equation and see the point of intersection of the graph to get the required value.

Hence, we see that the two lines intersect at (12,5.5)

Hence, cost of 1 bed sheet= $ 12

and cost of 1 towel= $ 5.50

Answer 2

Let x be the cost of each bed sheet and y be the cost of each of the towel. The system of linear equations that best represent the given condition is,
38x + 61y = 791.50
54x + 50y = 923
Solving for x and y in the equation gives, x = 12 and y = 5.5. Thus, one bedsheet costs $12 and each towel costs $5.5.