if i want to buy book for 5 friends and paperbacks cost $6.95 and hardbacks cost $24.99 how do i write and simplify an expression for the total amount spent

Question

 trying to solve a word problem

Answer 1

This one is a two-step process: first, understand and define your variables; then, put it all together!

It looks like you've got paperback or hardback books to choose from. Let's define a variable P that refers to the number of paperback books you buy. Since you're buying 5 books in total, then H (the number of hardback books) plus P (the number of paperback books) should equal 5. In other words: H + P = 5 or H = 5 - P

Total amount spent is the number of books times the cost per book. In our case, we have two sets:

Total amount spent (paperback) = $6.95 (cost of 1 paperback) x P (number of paperbacks)

Total amount spent (hardback) = $24.99 (cost of 1 hardback) x 5 - P (number of hardbacks)

Total amount spent (both books) = $6.95 x P + $24.99 x (5-P)

And there you have it - one expression for the total cost with only one variable (P).