Hanson is at a ball game with his family. He goes to the concession stand to buy soft pretzels and water bottles for everyone. A water bottle costs 2$, and a pretzel costs 3.50$. Hanson buys 16 items and spends 47$ in all.This system of equations can be used to represent the situation:x+y=162x+3.5y=47Which statement is correct?(A) In the system of equations, x represents the amount of money Hanson spends on pretzels, and y represents the amount of money he spends on water bottles.(B) In the system of equations, x represents the number of water bottles Hanson buys, and y represents the number of pretzels he buys.(C) In the system of equations, x represents the number of pretzels Hanson buys, and y represents the number of water bottles he buys.(D) In the system of equations, x represents the amount of money Hanson spends on water bottles, and y represents the amount of money he spends on pretzels.How much money does Hanson spend on pretzels?3.50$23.50$3
Q. Hanson is at a ball game with his family. He goes to the concession stand to buy soft pretzels and water bottles for everyone. A water bottle costs 2$, and a pretzel costs 3.50$. Hanson buys 16 items and spends 47$ in all.This system of equations can be used to represent the situation:x+y=162x+3.5y=47Which statement is correct?(A) In the system of equations, x represents the amount of money Hanson spends on pretzels, and y represents the amount of money he spends on water bottles.(B) In the system of equations, x represents the number of water bottles Hanson buys, and y represents the number of pretzels he buys.(C) In the system of equations, x represents the number of pretzels Hanson buys, and y represents the number of water bottles he buys.(D) In the system of equations, x represents the amount of money Hanson spends on water bottles, and y represents the amount of money he spends on pretzels.How much money does Hanson spend on pretzels?3.50$23.50$3
Identify Variables: First, identify what x and y represent in the system of equations. From the choices given, (B) is correct: x represents the number of water bottles Hanson buys, and y represents the number of pretzels Hanson buys.
Set Up Equations: Set up the equations based on the problem statement:1. x+y=16 (Total items bought)2. 2x+3.5y=47 (Total cost of items)
Solve for x: Solve the first equation for x:x=16−y
Substitute x: Substitute x in the second equation:2(16−y)+3.5y=4732−2y+3.5y=47
Combine Like Terms: Combine like terms:1.5y+32=47
Solve for y: Solve for y:1.5y=47−321.5y=15
Find y Value: Divide both sides by 1.5 to find y:y=1.515y=10
Substitute y: Substitute y back into the equation for x:x=16−10x=6
Calculate Total Cost: Calculate the total cost spent on pretzels:Cost of pretzels = 3.5×yCost of pretzels = 3.5×10Cost of pretzels = 35 (\$)
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