Answer:
35 cups of tea were sold and 20 cups of coffee were sold.
Step-by-step explanation:
We could put all of this information into a system of two equations. Lets make the variable t equal to the cups of tea sold and the variable c equal to the cups of coffee sold.
The equations are:
t + c = 55
5t + 3c = 235
There are many ways to solve for t and c at this point, but I am going to use the method of solving by substitution.
We can change the equation t + c = 55 into t = 55 - c. We can plug 55 - c in for t in the equation 5t + 3c = 235:
5(55 - c) + 3c = 235
Now solve for c. Distribute the 5 in 5(55 - c).
5(55) - 5c + 3c = 235
Simplify.
275 - 2c = 235
Subtract 275 from both sides of the equation.
275 - 2c - 275 = 235 - 275
Simplify.
-2c = -40
Divide -2 from both sides.
-2c ÷ (-2) = -40 ÷ (-2)
Simplify.
c = 20
So now we know that c = 20, so the cups of coffee sold is 20. Now we have to find the cups of tea sold. We can do this by plugging 20 for c in the equation t + c = 55:
t + 20 = 55
Solve for t. Subtract 20 from both sides.
t + 20 - 20 = 55 - 20
Simplify.
t = 35
So now we know that the cups of tea sold is 45.
35 cups of tea were sold and 20 cups of coffee were sold.
I hope you find this helpful. If you need clarifications on anything, feel free to ask me. Happy studying. :)
