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)

Question

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)

Answer 1

Let x be the number of hot dogs and y be the number of pretzels. We have two equations:

x + y = 300 (total items)
4x + 2y = 800 (total income)

We can solve this system of equations using substitution or elimination. Let's use elimination:

We can first rewrite the first equation as:

y = 300 - x

Now we can substitute this expression for y into the second equation:

4x + 2(300 - x) = 800

4x + 600 - 2x = 800

2x = 200

x = 100

Now we can find y:

y = 300 - 100

y = 200

So the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.

Answer 2

Let's assume the number of hot dogs to be sold is represented by "x" and the number of pretzels to be sold is represented by "y".

The revenue from selling hot dogs can be calculated by multiplying the number of hot dogs by the selling price: 4x.
Similarly, the revenue from selling pretzels is given by multiplying the number of pretzels by the selling price: 2y.

According to the problem, the revenue from selling both hot dogs and pretzels should be $800. So, we can write the equation:
4x + 2y = 800.

We also know that the total number of hot dogs and pretzels in stock is 300. So, we can write another equation:
x + y = 300.

We now have a system of equations:

4x + 2y = 800
x + y = 300

To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination to solve it.

Multiply the second equation by 2:
2x + 2y = 600.

Now, subtract the above equation from the first equation:
4x + 2y - (2x + 2y) = 800 - 600
4x - 2x + 2y - 2y = 200
2x = 200
x = 100.

Substituting the value of x into the second equation:
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.

Answer 3

To find out how many hot dogs and pretzels the boosters need to sell, we can set up a system of equations.

Let x represent the number of hot dogs sold and y represent the number of pretzels sold.

The revenue from the hot dogs would be 4x dollars, and the revenue from the pretzels would be 2y dollars.

According to the problem, the total revenue earned from selling hot dogs and pretzels should be $800. So, we can set up the following equation:

4x + 2y = 800

We also know that the total number of hot dogs and pretzels in stock is 300. Therefore, the total number of items sold can be represented as:

x + y = 300

Now we can solve this system of equations to find the values of x and y.

We'll use the method of substitution to solve the system.

First, let's solve the second equation for x:

x = 300 - y

Now substitute this value of x in the first equation:

4(300 - y) + 2y = 800

Simplifying the equation:

1200 - 4y + 2y = 800
-2y = 800 - 1200
-2y = -400

Divide both sides of the equation by -2:

y = -400 / -2
y = 200

Now substitute the value of y back into x + y = 300:

x + 200 = 300
x = 300 - 200
x = 100

So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.