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Corey owns a food truck that sells tacos and burritos. He only has enough supplies to make 81 tacos or burritos. He sells each taco for
$5 and each burrito for
$7.50. Corey must sell a minimum of
$510 worth of tacos and burritos each day. If 47 burritos were sold, determine all possible values for the number of tacos that Corey must sell in order to meet the requirements.
Answer:

Corey owns a food truck that sells tacos and burritos. He only has enough supplies to make $81$ tacos or burritos. He sells each taco for $\$ 5$ and each burrito for $\$ 7.50$ . Corey must sell a minimum of $\$ 510$ worth of tacos and burritos each day. If $47$ burritos were sold, determine all possible values for the number of tacos that Corey must sell in order to meet the requirements. $\newline$ Answer:

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Full solution

Q. Corey owns a food truck that sells tacos and burritos. He only has enough supplies to make

81

tacos or burritos. He sells each taco for

\$ 5

and each burrito for

\$ 7.50

. Corey must sell a minimum of

\$ 510

worth of tacos and burritos each day. If

47

burritos were sold, determine all possible values for the number of tacos that Corey must sell in order to meet the requirements.

\newline

Answer:

Calculate Total Sales: Corey sells burritos for \$\(7\).\(50\) each. If he sold \(47\) burritos, we need to calculate the total sales from the burritos.\(\newline\)Total sales from burritos = Number of burritos sold \(\times\) Price per burrito\(\newline\)Total sales from burritos = \(47 \times \$7.50\)\(\newline\)Total sales from burritos = \$\(352\).\(50\)
Find Additional Sales: Corey needs to make a minimum of \(\$510\) in sales each day. We have the sales from burritos, so we need to find out how much more he needs to make from selling tacos to reach the minimum sales requirement.\(\newline\)Minimum additional sales required from tacos = Minimum total sales required - Sales from burritos\(\newline\)Minimum additional sales required from tacos = \(\$510\) - \(\$352.50\)\(\newline\)Minimum additional sales required from tacos = \(\$157.50\)
Calculate Tacos Required: Corey sells each taco for \$\(5\). To find out the minimum number of tacos he needs to sell to make the additional \$\(157\).\(50\), we divide the additional sales required by the price per taco.\(\newline\)Number of tacos required = Minimum additional sales required from tacos / Price per taco\(\newline\)Number of tacos required = \$\(157\).\(50\) / \$\(5\)\(\newline\)Number of tacos required = \(31\).\(5\)\(\newline\)Since Corey cannot sell half a taco, he needs to sell at least \(32\) tacos to meet the minimum sales requirement.
Check Total Items: Corey has enough supplies to make a total of \(81\) tacos or burritos. He has already sold \(47\) burritos, so we need to check if selling \(32\) tacos will exceed the total number of items he can make.\(\newline\)Total items sold \(=\) Number of burritos sold \(+\) Number of tacos required to sell\(\newline\)Total items sold \(= 47 + 32\)\(\newline\)Total items sold \(= 79\)
Meet Minimum Sales: Since the total number of items sold (\(79\)) does not exceed the total number of items Corey can make (\(81\)), Corey can meet the minimum sales requirement by selling at least \(32\) tacos along with the \(47\) burritos.

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