Create and solve a system of equations for the following scenario: Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they have sold a total of 45 items and earned $195. If hot dogs cost $4 and hamburgers cost $5, how many did they sell of each?

Question

Mathematics

Armani Lin

23 September, 01:25

Create and solve a system of equations for the following scenario: Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they have sold a total of 45 items and earned $195. If hot dogs cost $4 and hamburgers cost $5, how many did they sell of each?

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Helen Craig · Answer 1

So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 - x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get - 1/5x = 6. Divide by - 1/5 to get x = - 30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4 (30) + 15 (5) = 195, or 120 + 75 = 195.