Answer:
b)
x = 3 hotdogs
y = 7 hamburgers
Explanation:
Steve went to the concession stand and bought hamburgers and hot dogs for the kids he brought to watch a baseball game. Each child chose either one hamburger or one hotdog. Hot dogs cost $1.50 each and hamburgers cost $2.75 each. Steve spent a total of $23.75 on 10 kids.
(a) Could Steve have bought an equal amount of hamburgers and hot dogs? Justify your answer.
An
(b) If x represents the number of hotdogs purchased and y represents the number of hamburgers purchased, write a system of equations that models this situation and determine the number of both items bought.
Let:
x = the number of hotdogs purchased y = the number of hamburgers purchased
Since the number of kids = 10
Our system for Equation is given as:
x + y = 10...... Equation 1
x = 10 - y
x × $1.50 + y × $2.75 = $23.75
1.5x + 2.75y = 23.75
Let us substitute 10 - y for x in Equation 2
1.5(10 - y) + 2.75 = 23.75
15 - 1.5y + 2.75y = 23.75
- 1.5y + 2.75y = 23.75 - 15
1.25y = 8.75
y = 8.75/1.25
y = 7 hamburgers
Solving for x
x = 10 - y
x = 10 - 7
x = 3 hotdogs
Therefore,
x = 3 hotdogs
y = 7 hamburgers