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](https://img.qammunity.org/2022/formulas/mathematics/high-school/orn14wuvws39pr7tztmk0yb08u2s1naar5.png)
![p \le 4.76](https://img.qammunity.org/2022/formulas/mathematics/high-school/imy22ajaaufk6isjacaf2rht9d87l1r27l.png)
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](https://img.qammunity.org/2022/formulas/mathematics/high-school/c3qcqmyl9wrhmlh5biky0duj5nlxp469ps.png)
![15.0 + 10.50p \le 65](https://img.qammunity.org/2022/formulas/mathematics/high-school/orn14wuvws39pr7tztmk0yb08u2s1naar5.png)
Solving further:
![10.50p \le 65 - 15.0](https://img.qammunity.org/2022/formulas/mathematics/high-school/k6eub3zp6y424qkwev8p9we1lryu28r0cv.png)
![10.50p \le 50.0](https://img.qammunity.org/2022/formulas/mathematics/high-school/iq81xa8wjv61e65bci2jcnmkcer0iizgqi.png)
Make p the subject
![p \le (50.0)/(10.50)](https://img.qammunity.org/2022/formulas/mathematics/high-school/kq7t3hh5r5p62gofuxaert8twsvybeomcg.png)
-- approximated