Devon and his friends bought strawberry wafers for $3 per packet and chocolate wafers for $1 per packet at a carnival. They spen
t a total of $30 to buy a total of 22 packets of wafers of the two varieties. Part A: Write a system of equations that can be solved to find the number of packets of strawberry wafers and the number of packets of chocolate wafers that Devon and his friends bought at the carnival. Define the variables used in the equations. (5 points)
Part B: How many packets of chocolate wafers and strawberry wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)
PART A: The system of equations we would use would be: x + y = 22 (amount of items) 3x + 1y = 30 (cost)
Variables: x = the amount of strawberry wafers bought at the price of $3 y = the amount of chocolate wafers bought at the price of $1
PART B: To solve, we'll use substitution because we can easily isolate a variable using the first equation.
Work: x + y = 22 (first equation) y = 22 - x (isolating a variable) 3x + 1y = 30 (second equation) 3x + (22 - x) = 30 (substituting into the second equation) 2x + 22 = 30 (simplifying) 2x = 8 (subtracting) x = 4 strawberry wafers 4 + y = 22 (substituting x into the first equation to solve for y) y = 18 chocolate wafers
ANSWER: They bought 4 strawberry wafers and 18 chocolate wafers.
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