Please show me how to calculate this problem: The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $3.20. Today they made $99.20 from the 42 wraps sold. How many of the wraps sold were vegetarian?
total sales:
total wraps:
1.00v + 3.20c = 99.20
v + c = 42
subtract one equation from the other:
2.20c = 57.20
c = 26
so, v = 16
To solve this problem, we need to set up a system of equations. Let x represent the number of vegetarian wraps sold and y represent the number of chicken wraps sold.
1) The total number of wraps sold is 42:
x + y = 42
2) The total amount of money made is $99.20:
1.00x + 3.20y = 99.20
To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution.
From equation 1, we can solve for y in terms of x:
y = 42 - x
Substitute this value of y into equation 2:
1.00x + 3.20(42 - x) = 99.20
Simplify the equation:
1.00x + 134.40 - 3.20x = 99.20
Combine like terms and solve for x:
-2.20x = -35.20
x = -35.20 / -2.20
x = 16
Therefore, the number of vegetarian wraps sold is 16.
To solve this problem, we can use a system of equations. Let's assign variables to the number of vegetarian wraps and the number of chicken wraps sold.
Let's say the number of vegetarian wraps sold is x, and the number of chicken wraps sold is y.
According to the information provided, the cost of a vegetarian wrap is $1.00, and the cost of a chicken wrap is $3.20. We also know that they made a total of $99.20 from the wraps sold.
Using this information, we can set up two equations:
Equation 1: x + y = 42 (since the total number of wraps sold is 42)
Equation 2: 1.00x + 3.20y = 99.20 (since the total cost of the wraps sold is $99.20)
To solve this system of equations, we can use any method, such as substitution or elimination. Let's use the substitution method:
From Equation 1, we can express y in terms of x: y = 42 - x.
Substituting this value of y into Equation 2, we get:
1.00x + 3.20(42 - x) = 99.20
1.00x + 134.40 - 3.20x = 99.20
Simplifying the equation, we have:
-2.20x + 134.40 = 99.20
Now, let's isolate the variable x:
-2.20x = 99.20 - 134.40
-2.20x = -35.20
x = -35.20 / -2.20
x = 16
Therefore, the number of vegetarian wraps sold is 16.