Charlene owns a bookstore. She purchases used books from customers. • She pays $3.50 for each hardback book. • She pays $0.75 for each paperback book. • Charlene pays a customer a total of $199.75 for 149 used books. Which system of equations could be used to determine the number of hardback books (x) and the number of paperback books (y) Charlene purchases from the customer?

Number of hardback = 32

Number of paperback = 117

Step-by-step explanation:

Let the number of hardback books be represented by x.

Let the number of paperback books be represented by y.

Based on the information given, we can form an equation which will be:

x + y = 149 i

3.50x + 0.75y = 199.75 ii

Multiply equation i by 3.50

Multiply equation ii by 1

3.50x + 3.50y = 521.50 iii

3.50x + 0.75y = 199.75 iv

Subtract equation iv from iii

2.75y = 321.75

y = 321.75 / 2.75

y = 117

Number of paperback = 117

Since x + y = 149

x = 149 - y

x = 149 - 117

x = 32

Number of hardback = 32

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints