Mr. Christian, the owner of two car dealerships in Westford, is holding a contest to see which one can sell the most cars. Westford Cars has already sold 20 cars, and Christian's Autos has sold 2 cars. Going forward, the salespeople at Westford Cars think they can sell 1 car per day, whereas the salespeople at Christian's Autos are aiming for sales of 4 cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How long will that take? How many cars will each lot have sold?
To determine how long it will take for the two dealerships to be tied, we can set up an equation:
20 + 1x = 2 + 4x
Where x is the number of days it takes for the two dealerships to be tied.
Simplifying the equation, we have:
1x - 4x = 2 - 20
-3x = -18
x = 6
Therefore, it will take 6 days for the two dealerships to be tied.
To calculate the number of cars each lot will have sold after 6 days, we can substitute x into the equation:
20 + 1(6) = 26
2 + 4(6) = 26
Therefore, both Westford Cars and Christian's Autos will have sold 26 cars each after 6 days.
The Rushwood Elementary School PTA is hosting a “Donuts with Dad” breakfast for the Kindergarten students. They have asked the Donut Factory for pricing to cater the event. Below are two options the Donut Factory provided the PTA:
Package 1: Base fee of $20 plus $1.50 per person
Package 2: $2.50 per person
Let x represent the number of people attending the breakfast, and y represent the total cost of the breakfast. Which of these systems of equations could be used to model the two package options?
To model the two package options, we can set up a system of equations based on the given information.
Let x represent the number of people attending the breakfast, and y represent the total cost of the breakfast.
For Package 1, the base fee is $20, and there is an additional charge of $1.50 per person. Therefore, the equation for Package 1 would be:
y = 20 + 1.50x
For Package 2, there is a charge of $2.50 per person, so the equation for Package 2 would be:
y = 2.50x
So the system of equations to model the two package options would be:
Package 1: y = 20 + 1.50x
Package 2: y = 2.50x
Given the two packages from the Donut Factory, and your answer to Part A, how much would it cost if the PTA chose package 1, and 63 people came to the breakfast?
Package 1: Base fee of $20 plus $1.50 per person
Package 2: $2.50 per person
To calculate the cost if the PTA chose package 1 and 63 people came to the breakfast, we can use the equation for Package 1:
y = 20 + 1.50x
Substituting x = 63 into the equation:
y = 20 + 1.50(63)
y = 20 + 94.5
y = 114.5
Therefore, if the PTA chose package 1 and 63 people came to the breakfast, it would cost $114.50.
A theater sold 160 children's tickets and 90 adult tickets.An adult ticket plus a children's ticket equals $13.50. If the theater made $1,600 from the sales of the tickets, what were the prices of each ticket?
Let's assume the price of a children's ticket is 'C' dollars and the price of an adult ticket is 'A' dollars.
According to the given information, the theater sold 160 children's tickets and 90 adult tickets. So, we can set up two equations based on the number of tickets sold:
160C + 90A = 1600 (Equation 1)
C + A = 13.50 (Equation 2)
We can solve this system of equations to find the prices of each ticket.
First, let's solve Equation 2 for C:
C = 13.50 - A
Substitute this expression for C in Equation 1:
160(13.50 - A) + 90A = 1600
2160 - 160A + 90A = 1600
-70A = -560
A = 8
Substitute the value of A back into Equation 2 to find the value of C:
C + 8 = 13.50
C = 13.50 - 8
C = 5.50
Therefore, the price of a children's ticket is $5.50 and the price of an adult ticket is $8.