he manager at a coffee stand keeps track of the number of cups of coffee and cups of tea sold each day and the total money received. On Friday, a total of 55 cups were sold, and the money collected was $235. If cups of coffee are sold for $5 and cups of tea are sold for $3, how many cups of coffee and cups of tea were sold?

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. :)