Respuesta :
Answer:
[tex]10.50p+15\leq 65[/tex]
[tex]p\leq \frac{100}{21}[/tex]
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 [tex]\$7.50\times 2=\$15[/tex].
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 [tex]10.50p[/tex].
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:
[tex]10.50p+15\leq 65[/tex]
Therefore, our required inequality would be [tex]10.50p+15\leq 65[/tex].
[tex]10.50p+15-15\leq 65-15[/tex]
[tex]10.50p\leq 50[/tex]
Divide both sides by 10.50:
[tex]\frac{10.50p}{10.50}\leq \frac{50}{10.50}[/tex]
[tex]p\leq \frac{50*2}{10.50*2}[/tex]
[tex]p\leq \frac{100}{21}[/tex]
[tex]p\leq 4.76190[/tex]
Therefore, Lydia can buy less than or equal to [tex]\frac{100}{21}[/tex] pounds of Pumpkin Spice coffee.
