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

10.50p+15≤65

p≤ 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,socostof′ p'

pounds of Pumpkin Spice coffee would be 10.50

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≤65

Therefore, our required inequality would be 10.50p+15≤65

10.50+15-15≤65-75

10.50≤50

Divide both sides by 10.50:

10.50p/10.50 ≤ 50/10.50

P ≤ 50*2/10.50*2

P ≤ 100/21

P ≤ 4.76190

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