Question

PLEASE HELP ME ANY ANSWERS PLEASEEEE I DONT UNDERSTAND THIS!!!!!) Marina wants to purchase a rosebush for d dollars at a garden store. She has a coupon good for $5 off her purchase, and the store is having a 10% off sale.

PART A
write two different, equivalent expressions for how much the rosebush will cost if the coupon is applied first and the 10% discount second.
PART B
write an expression for how much the rosebush will cost if the 10% discount is applied first and the coupon is applied second.
PART C
which order will save marina more money? explain your reasoning.

Answer 1

PART A:
`0.9(d-5)` and
`0.9d-4.5`

If we apply the coupon first, we have
`d-5`, because we are subtracting 5 dollars from the total price. Then, if we apply the discount, we get
`0.9(d-5)`. It is a 10% discount, which means the price will end up being 90% of the original price, so we need to multiply the price by 0.9. To get the second equation, I distributed the 0.9 (multiplied it by both parts of the equation in parentheses) to get
`0.9d-4.5`.

PART B:
`0.9d-5`

If we apply the discount first, we get
`0.9d`. Then, when we apply the coupon, we subtract 5 dollars from that price, getting
`0.9d-5`.

PART C: Discount, then coupon.

To figure out which order will save more money, we look at the simplified equations for each order. In the first order, we end up subtracting 4.5 from
`0.9d`, and in the second order, we end up subtracting 5 from
`0.9d`. In the second order, we are subtracting more money, so the price will be lower and she will save more money.