Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Scouting troops in Marshall County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 15 crab meals and 17 vegetarian meals, with total receipts of $890. Another sold tickets for 16 crab meals and 17 vegetarian meals, bringing in a total of $921. How much do the two types of tickets cost? A ticket for a crab meal costs $_____, and a ticket for a vegetarian meal costs $_____.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  Scouting troops in Marshall County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 15 crab meals and  17 vegetarian meals, with total receipts of $890. Another sold tickets for 16 crab meals and  17 vegetarian meals, bringing in a total of $921. How much do the two types of tickets cost?  A ticket for a crab meal costs $_____, and a ticket for a vegetarian meal costs $_____.

Bytelearn · Accepted Answer

Define Equations: Let's denote the cost of a crab meal ticket as $ c $ and the cost of a vegetarian meal ticket as $ v $. We can then write two equations based on the information given: 1. For the first troop member: $ 15c + 17v = 890 $ 2. For the second troop member: $ 16c + 17v = 921 $Eliminate Variable: To solve this system using elimination, we need to eliminate one of the variables. We can subtract the first equation from the second to eliminate $ v $: $ (16c + 17v) - (15c + 17v) = 921 - 890 $Find Cost of Crab Meal: Simplifying the subtraction, we get: $ 16c - 15c + 17v - 17v = 921 - 890 $ $ c = 31 $ So, a ticket for a crab meal costs $31.Substitute and Solve: Now that we know the cost of a crab meal ticket, we can substitute $ c = 31 $ into one of the original equations to find $ v $. Let's use the first equation: $ 15(31) + 17v = 890 $Calculate Vegetarian Meal Cost: Calculating the multiplication, we get: $ 465 + 17v = 890 $ Now, we need to isolate $ v $ by subtracting 465 from both sides of the equation: $ 17v = 890 - 465 $Performing the subtraction, we find: $ 17v = 425 $ To find $ v $, we divide both sides by 17: $ v = \frac{425}{17} $Calculating the division, we get: $ v = 25 $ So, a ticket for a vegetarian meal costs $25.

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