Question

Lydia is at a coffee shop and knows

she can spend no more than $65

before tax. She sees this price list in

the coffee shop.

Item

Dark Roast Coffee

Pumpkin Spice Coffee

Breakfast Tea

Price per pound

$7.50

$10.50

$23.50

Part A

Write a number in each blank to complete an inequality Lydia can use to find how

many pounds of Pumpkin Spice coffee, p, she can buy along with 2 pounds of

Dark Roast coffee.

Answer 1

4 pounds of pumpkin spice coffee

Answer 2

`10.50p+15\leq 65`

`p\leq (100)/(21)`

Explanation:

Let p represent pounds of Pumpkin Spice coffee.

We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.

Item Price per pound

Dark Roast Coffee $7.50

Pumpkin Spice Coffee $10.50

Breakfast Tea $23.50

Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be
`\$7.50* 2=\$15`.

We are told that cost of each pound of Pumpkin Spice coffee is $10.50, so cost of 'p' pounds of Pumpkin Spice coffee would be
`10.50p`.

Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.

We can represent this information in an inequality as:

`10.50p+15\leq 65`

Therefore, our required inequality would be
`10.50p+15\leq 65`.

`10.50p+15-15\leq 65-15`

`10.50p\leq 50`

Divide both sides by 10.50:

`(10.50p)/(10.50)\leq (50)/(10.50)`

`p\leq (50*2)/(10.50*2)`

`p\leq (100)/(21)`

`p\leq 4.76190`

Therefore, Lydia can buy less than or equal to
`(100)/(21)` pounds of Pumpkin Spice coffee.