The Baynard High School Boosters are selling hot dogs and pretzels at the concession stand. They have 300 hot dogs and pretzels in stock and want to earn an income of $800. They plan to sell the hot dogs for $4 each and the pretzels for $2 each. How many hot dogs and how many pretzels do the boosters need to sell to reach their goal of $800? (1 point)
A. 250 hot dogs and 50 pretzels
B. 50 hot dogs and 250 pretzels
C. 200 hot dogs and 100 pretzels
D. 100 hot dogs and 200 pretzels
Let's assume the boosters sell x hot dogs and y pretzels.
The income from selling hot dogs is 4x dollars.
The income from selling pretzels is 2y dollars.
According to the problem, they want to earn a total income of 800 dollars.
So, the equation becomes:
4x + 2y = 800
However, we are also given that there are 300 hot dogs and pretzels in stock. So, the sum of the number of hot dogs and pretzels sold should be equal to 300.
So, the second equation becomes:
x + y = 300
Now we have a system of two equations:
4x + 2y = 800
x + y = 300
Multiplying the second equation by 2, we get:
2x + 2y = 600
Subtracting this equation from the first equation, we get:
2x = 200
x = 100
Substituting x = 100 into the second equation, we get:
100 + y = 300
y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
The correct answer is option D. 100 hot dogs and 200 pretzels.
Let's assume that the number of hot dogs sold is represented by "x" and the number of pretzels sold is represented by "y".
Based on the given information, we can set up two equations:
1. The total number of hot dogs and pretzels sold must be 300:
x + y = 300 (Equation 1)
2. The income earned from selling the hot dogs and pretzels must be $800:
4x + 2y = 800 (Equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's solve it using the elimination method.
Multiplying Equation 1 by 2, we get:
2x + 2y = 600 (Equation 3)
Subtracting Equation 3 from Equation 2, we can eliminate the 'y' variable:
(4x + 2y) - (2x + 2y) = 800 - 600
4x - 2x = 200
2x = 200
x = 100
Substituting this value of x into Equation 1, we can find the value of y:
100 + y = 300
y = 300 - 100
y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
So, the correct answer is:
D. 100 hot dogs and 200 pretzels.
To solve this problem, we can start by setting up a system of equations. Let's let "x" represent the number of hot dogs sold and "y" represent the number of pretzels sold.
From the given information, we know that the price of each hot dog is $4 and the price of each pretzel is $2. The boosters want to earn an income of $800.
The total income from selling hot dogs and pretzels can be expressed as:
Total Income = (Price of Hot Dogs) * (Number of Hot Dogs) + (Price of Pretzels) * (Number of Pretzels)
Using the values we have, the equation becomes:
800 = 4x + 2y
We also know that the boosters have 300 hot dogs and pretzels in stock. This means that the number of hot dogs and pretzels sold cannot exceed 300.
The equation for the limit on the number of items sold becomes:
x + y ≤ 300
Now we have a system of equations:
800 = 4x + 2y
x + y ≤ 300
To find the solution, we can solve this system of equations. One way to do this is by graphing the inequalities and finding the region that satisfies both constraints. However, since the answer choices are given in numerical form, we can simply substitute the values to check which combination satisfies both equations.
Let's substitute the values from each answer choice into the equations:
A. 250 hot dogs and 50 pretzels
800 = 4(250) + 2(50)
800 = 1000 (not true)
B. 50 hot dogs and 250 pretzels
800 = 4(50) + 2(250)
800 = 400 + 500
800 = 900 (not true)
C. 200 hot dogs and 100 pretzels
800 = 4(200) + 2(100)
800 = 800 (true)
D. 100 hot dogs and 200 pretzels
800 = 4(100) + 2(200)
800 = 400 + 400
800 = 800 (true)
By substituting the values for choices C and D, we find that both combinations of 200 hot dogs and 100 pretzels, or 100 hot dogs and 200 pretzels, satisfy the given conditions.
Therefore, the answer is:
C. 200 hot dogs and 100 pretzels
D. 100 hot dogs and 200 pretzels