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 $800? say you had 300 of x and 300 of y and you needed to get 800 dollars from both x and y, if they sold x for 4$ and y for 2$ how many of of x and y do they need to sell
Let x be the number of hot dogs and y be the number of pretzels. We have:
x + y = 300 (since they have 300 hot dogs and pretzels in stock)
4x + 2y = 800 (since they want to earn $800 from selling hot dogs and pretzels)
To solve this system of equations, we can use the substitution method. We can solve the first equation for y:
y = 300 - x
Now, substitute this expression for y in the second equation:
4x + 2(300 - x) = 800
Simplify and solve for x:
4x + 600 - 2x = 800
2x = 200
x = 100
Now that we have the value of x, use it to find the value of y:
y = 300 - 100
y = 200
So the boosters must sell 100 hot dogs (x) and 200 pretzels (y) to reach their goal of $800.
Let's assume the number of hot dogs the boosters need to sell is 'x', and the number of pretzels they need to sell is 'y'.
We know that the boosters have 300 hot dogs and pretzels in stock, so we can write the equation:
x + y = 300
The income from selling the hot dogs is $4 multiplied by the number of hot dogs sold, which is 'x'. Similarly, the income from selling the pretzels is $2 multiplied by the number of pretzels sold, represented by 'y'. The total income is given as $800. So we can write another equation:
4x + 2y = 800
Now we have a system of equations. We can solve these equations simultaneously to find the values of 'x' and 'y'.
First, let's solve the equation x + y = 300 for 'x':
x = 300 - y
Substituting this value of 'x' into the second equation, we get:
4(300 - y) + 2y = 800
Expanding the equation:
1200 - 4y + 2y = 800
Simplifying the equation:
-2y = 800 - 1200
-2y = -400
y = -400 / -2
y = 200
Substituting the value of 'y' back into the equation x + y = 300, we can find 'x':
x + 200 = 300
x = 300 - 200
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
To solve this problem, let's use algebra to represent the number of hot dogs and pretzels sold.
Let's assume the number of hot dogs sold is represented by 'x' and the number of pretzels sold is represented by 'y'.
Given that 300 hot dogs and pretzels are in stock, we have two equations:
x + y = 300 (equation 1) (represents the total number of hot dogs and pretzels sold)
The income earned from selling hot dogs and pretzels can be represented by the equation:
4x + 2y = 800 (equation 2) (represents the income earned from selling hot dogs and pretzels)
Now we have a system of two equations. To solve it, we can use a method called substitution or elimination.
Let's use the substitution method:
From equation 1, we can rewrite it as x = 300 - y.
Substitute this value of x into equation 2:
4(300 - y) + 2y = 800
Now simplify the equation:
1200 - 4y + 2y = 800
Combine like terms:
-2y = -400
Divide by -2 on both sides to solve for y:
y = 200
Now we know that 200 pretzels need to be sold.
To find the number of hot dogs, substitute the value of y (200) into equation 1:
x + 200 = 300
Subtract 200 from both sides:
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.