A movie theater sells popcorn and fountain drinks. Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50. Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75. If p represents the number of popcorn buckets and d represents the number of drinks, then the system of equations
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Question:
A movie theater sells popcorn and fountain drinks. Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50. Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75. If p represents the number of popcorn buckets and d represents the number of drinks, then the system of equations
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Answer: the systems of equations to solve the unit price of popcorn and rinks are 1 p + 3 d= 12.50---- equation 1 3 p + 4 d= 23.75 ---- equation 2 The price of A popcorn bucket = $4.25 and price of 1 fountain drink = $2.75Step-by-step explanation:Step 1 If p represents the number of popcorn buckets and d represents the number of drinks, The expression that Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50 becomes 1 p + 3 d= $12.50 and The expression that Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75 becomes 3 p + 4 d= $23.75 such that the systems of equations to solve the unit prices of popcorn and drinks are 1 p + 3 d= $12.50---- eqn 1 3 p + 4 d= $23.75 ---- eqn 2 Step 2 1 p + 3 d= $12.50---- eqn 1 3 p + 4 d= $23.75 ---- eqn 2 Multiplying equation 1 by( 3 ) 1 p + 3 d= $12.50---- eqn 1 x 33p+ 9d= 37.5----- equation 3 and subtracting equation 2 from equation 3 becomes3p+ 9d= 37.5----- equation 3 - 3 p + 4 d= $23.755d= 13.75d= 13.75/5d= 2.75 to find p, sinceaa d = 2.75, 1 p + 3 d= 12.50 1 p + 3 x 2.75= 12.50p= 12.50-8.25p=4.25 THerefore the price of popcorn = $4.25 and price of drinks = $2.75
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