Question

A bakery sells two types of cakes, chocolate and vanilla. The chocolate cakes sell for $5 each, and the vanilla cakes sell for $3 each. If the bakery sold a total of 50 cakes and earned $200 in total sales, how many of each type of cake did they sell?

Answer 1

Explanation:

Let's use "x" to represent the number of chocolate cakes sold and "y" to represent the number of vanilla cakes sold.

From the problem statement, we know that the bakery sold a total of 50 cakes, so we can set up an equation:

x + y = 50

We also know that the total sales were $200. If the chocolate cakes sold for $5 each and the vanilla cakes sold for $3 each, we can set up another equation for the total sales:

5x + 3y = 200

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = 50 - x

Substituting this expression for y into the second equation, we get:

5x + 3(50 - x) = 200

Simplifying this equation, we get:

2x + 150 = 200

2x = 50

x = 25

So the bakery sold 25 chocolate cakes. To find the number of vanilla cakes sold, we can substitute x = 25 into the equation y = 50 - x:

y = 50 - 25

y = 25

So the bakery also sold 25 vanilla cakes.

Therefore, the bakery sold 25 chocolate cakes and 25 vanilla cakes.