Question

you are online shopping on bed, bath and beyond’s website to replace the towels in your bathroom. you want to replace four full sets, which include wash cloth, hand towel and bath towel. one wash cloth costs $3.99, one hand towel $6.59 and one bath towel $9.99. you also decide to buy a matching bath mat for $11.99. at checkout you enter in your code for 15% off the most expensive item. how much did you pay? $

Answer 1

We want four full sets of wash cloth, hand towel and bath towel. The price for each set is given by the sum of the unitary price of each item

`3.99+6.59+9.99`

This is the price for one set. Since we want four sets, we just need to multiply this expression by 4.

`4(3.99+6.59+9.99)`

We're also going to buy a matching bath mat for $11.99. On this case, we just need to add the bath mat price to the expression

`4(3.99+6.59+9.99)+11.99_{}`

At checkout you enter in your code for 15% off the most expensive item. The most expensive item is the bath mat. Since the discount is 15% of the most expensive item, we just need to multiply the most expensive item cost by 0.15 and subtract from the total, and then, we're going to have our final expression for the price.

`P=4(3.99+6.59+9.99)+11.99_{}-11.99\cdot0.15`

If we expand this expression using the distributive rule, we can rewrite it as

`\begin{gathered} P=4(3.99+6.59+9.99)+11.99_{}-11.99\cdot0.15 \\ =4\cdot3.99+4\cdot6.59+4\cdot9.99+11.99_{}(1-0.15) \\ =4\cdot3.99+4\cdot6.59+4\cdot9.99+11.99_{}\cdot0.85 \end{gathered}`

And those are the two ways of writting the expression.

Evaluating this expression, we have

`\begin{gathered} P=4\cdot3.99+4\cdot6.59+4\cdot9.99+11.99_{}\cdot0.85=92.4715 \\ \approx92.47 \end{gathered}`