Suppose the central Park Coffee Shop sells a cup of expresso for 2.00 and a cup of cappuccino for 2.50. On Friday Destiny sold 30 more cups of cappuccino than expresso for a total of 178.50, worth of expresso and cappuccino. How many cups of each were sold?
I am learion to learning about weighted averages and we are suppose to make a chart and equation. I think my chart is right but i cant seem to make an equation that makes sense. Please please help me!!!!!!
C=E+30
2E+2.5C=178.5
Im sorry but i do not see how to solve. I just figured out that it is 53 cappuccinos and 23 expressos, but i can not make an equation that shows how I got those two numbers.
To solve this problem, we can use a system of equations. Let's start by assigning variables to the unknowns - the number of cups of espresso and cappuccino sold.
Let's say x represents the number of cups of espresso sold, and y represents the number of cups of cappuccino sold.
According to the problem, the price of an espresso cup is $2.00, so the total value of espresso cups sold would be 2x.
Similarly, the price of a cappuccino cup is $2.50, so the total value of cappuccino cups sold would be 2.50y.
We also know that Destiny sold 30 more cups of cappuccino than espresso, so we can write another equation as:
y = x + 30
Finally, the total value of espresso and cappuccino sold together is $178.50. Therefore, we can write the equation:
2x + 2.50y = 178.50
Now we have a system of two equations with two unknowns:
Equation 1: y = x + 30
Equation 2: 2x + 2.50y = 178.50
To solve this system, we can substitute the value of y from Equation 1 into Equation 2 and solve for x.
Substituting y = x + 30 into Equation 2 gives us:
2x + 2.50(x + 30) = 178.50
Now we can solve for x:
2x + 2.50x + 75 = 178.50
4.50x + 75 = 178.50
4.50x = 178.50 - 75
4.50x = 103.50
x = 103.50 / 4.50
x = 23
So, the number of cups of espresso sold is 23.
Substituting this value back into Equation 1 gives us:
y = 23 + 30
y = 53
Therefore, the number of cups of cappuccino sold is 53.
So, 23 cups of espresso and 53 cups of cappuccino were sold.