Question

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

Missing part of the 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 Price per pound

Dark Roast Coffee $7.50

Pumpkin Spice Coffee $10.50

Answer:

`15.0 + 10.50p \le 65`

`p \le 4.76`

Explanation:

From the question, we understand that she wants to buy 2 pounds of dark roast coffee.

If 1 pound costs $7.50, then 2 pounds cost $15.0 (i.e. $7.50 * 2)

If 1 pound of pumpkin spice coffee costs $10.50, then p pounds cost $10.50p (i.e. $10.50 * p)

So, her total spendings (before tax) is:

Spendings = 15.0 + 10.50p

We also know that she plans to spend not more than $65.

The inequality that represents this scenario is:

`Spendings \le 65`

`15.0 + 10.50p \le 65`

Solving further:

`10.50p \le 65 - 15.0`

`10.50p \le 50.0`

Make p the subject

`p \le (50.0)/(10.50)`

`p \le 4.76` -- approximated