How many of each type of book did Mrs Sign purchase?

Question

During the past year Mrs. Singh purchased 43 books. She purchased softcover books for $5.50 each and hardcover for $13.50 each. The total cost of the books was $396.50. How many of each type of book did she purchase?

Answer 1

Let X be softcover and Y be hardcover:

X+Y = 43  (She purchased 43 books total)

So Y = 43 - X

 

The equation for the cost is "Total cost = Softcover * cost of softcover  + Hardcover*cost of hardcover)

396.50 = X * 5.50 + Y*13.50

we know Y = 43-X and can plug that in:

396.50 = X*(5.50) + (43-X)*(13.50), (where X is the number of softcover)

now do the algebra:

396.5 = 5.50X + 43(13.50) - 13.50*X

396.5 = 580.5 - 8.00X

X = (396.5 - 580.5)/-8.00

X = 23

 

So Y = 43-X = 43-23 = 20!

 

X (softcovers) = 23

Y (hardcovers) = 20

 

You can double check by pluggin back into the equation 396.5 = X*5.50 + Y*13.50  !