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:

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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:

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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. Total sales from burritos = Number of burritos sold × Price per burrito Total sales from burritos = 47 × $7.50 Total sales from burritos = $352.50Find 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. Minimum additional sales required from tacos = Minimum total sales required - Sales from burritos Minimum additional sales required from tacos = $510 - $352.50 Minimum additional sales required from tacos = $157.50Calculate 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. Number of tacos required = Minimum additional sales required from tacos / Price per taco Number of tacos required = $157.50 / $5 Number of tacos required = 31.5 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. Total items sold = Number of burritos sold + Number of tacos required to sell Total items sold = 47 + 32 Total items sold = 79Meet 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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