Question

Lydia is at a coffee shop and knows

Answer 1

Answer:

$10.50p+15\leq 65$

$p\leq \frac{100}{21}$

Step-by-step 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 $\ 7.50\times 2=\ 15$.

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:

$\frac{10.50p}{10.50}\leq \frac{50}{10.50}$

$p\leq \frac{50*2}{10.50*2}$

$p\leq \frac{100}{21}$

$p\leq 4.76190$

Therefore, Lydia can buy less than or equal to $\frac{100}{21}$ pounds of Pumpkin Spice coffee.