Question

((Please help :D)) All the books at a store have the same price. The store is having a sale advertised with “buy one book, get the second half off.”

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a) Write an expression with two terms to represent the cost of buying two books during the sale.
b) Write an equivalent expression with only one term.

Answer 1

Part A

Let x be the cost of one book (before any kind of discount is applied). The first book is x dollars. The second book will be x/2 dollars since we get the second book half off. This is another way of saying a discount of 50%. We can write x/2 as (1/2)x or 0.5x; so there are multiple ways to answer. Probably the easiest to write out would be 0.5x

From here, we add the two costs x and 0.5x to get x+0.5x

We do not combine like terms, as that will happen with part B

Answer: x+0.5x

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Part B

We'll use the result of part A.

Think of the first x as 1x. It's saying we have one copy of x

So x+0.5x is the same as 1x+0.5x

Then to combine like terms, we add the numbers 1 and 0.5 to get 1.5

So 1x+0.5x = 1.5x

We can use the distributive property to see that

1x+0.5x = (1+0.5)x = 1.5x

Or you can think of it like saying "we have one x and half an x added, so overall we have one and a half x's"

However method you use, the answer from part A combines to 1.5x

If you want a fraction form, then it would be (3/2)x since 3/2 = 1.5; though I find decimals to be easier to work with.

Answer: 1.5x