Liam is selling cookies at a bake sale. He spent $50 on supplies and will sell the cookies for $2 each. He would like to have a profit of more than $80. Which inequality can be used to find the number of cookies that Liam needs to sell.

The fixed cost here is '$50' whilst the profit required to be made must be greater than $80 , moreover the selling price of cookie being $2 makes the expression for the revenue out of selling per cookie equal to '2c'.

thus,our inequality would be ,

2c - 50 > 80
2c -50 + 50 > 80 + 50
2c > 130
c > 130/2
c > 65

therefore, the inequality that represents the number of cookies that Liam needs to sell is c > 65 i.e. he needs to sell more than 65 cookies in order to make a profit of a sum more than $80.

msm555 msm555 · Answer 2 · 2024-02-02T16:18:38+01:00

Answer:

Inequality: [tex] 2x - 50 > 80 [/tex]

[tex] x > 65 [/tex]

Step-by-step explanation:

To find the number of cookies that Liam needs to sell in order to achieve a profit of more than $80, we can set up an inequality.

Let [tex] x [/tex] represent the number of cookies Liam needs to sell.

Liam's profit is the total revenue minus the total cost. The total revenue is the price of each cookie ($2) times the number of cookies sold ([tex] x [/tex]).

The total cost includes the $50 spent on supplies.

The inequality for Liam's profit can be written as:

[tex] \textsf{Profit} > \$80 [/tex]

[tex] (\textsf{Revenue}) - (\textsf{Cost}) > \$80 [/tex]

[tex] (2x) - (50) > 80 [/tex]

Now, we can solve for [tex] x [/tex]:

[tex] 2x - 50 > 80 [/tex]

Add 50 to both sides:

[tex] 2x -50+50 > 80 + 50 [/tex]

[tex] 2x > 130 [/tex]

Divide both sides by 2:

[tex] \dfrac{2x}{2} > \dfrac{130}{2} [/tex]

[tex] x > 65 [/tex]

So, Liam needs to sell more than 65 cookies to achieve a profit of more than $80.

Therefore, the inequality that can be used to find the number of cookies Liam needs to sell is:

[tex] x > 65 [/tex]