Question

At Darling Donuts, a dozen glazed donuts costs $3.50, and a dozen chocolate donuts costs $6.25. Yesterday, the number of dozens of chocolate donuts sold was seven more than three times the number of dozens of glazed donuts sold, and a total of 199 dozen donuts were sold. Is it possible that the store earned a total of $1,037.50 from selling 75 dozen glazed donuts and 124 dozen chocolate donuts yesterday?

Answer 1

Let’s see if the store earned a total of $1,037.50 from selling 75 dozen glazed donuts and 124 dozen chocolate donuts yesterday.

First, we need to find the number of dozens of glazed donuts and chocolate donuts sold yesterday using the given information. We can use the following system of equations to do that:

x+y=199
y=3x+7​

where x is the number of dozens of glazed donuts and y is the number of dozens of chocolate donuts.

To solve this system, we can substitute y with 3x+7 in the first equation and get:

x+(3x+7)=199

Simplifying and solving for x, we get:

4x+7=1994x=192x=48

So, the number of dozens of glazed donuts sold yesterday was 48. To find the number of dozens of chocolate donuts, we can plug in x=48 into the second equation and get:

y=3(48)+7y=151

So, the number of dozens of chocolate donuts sold yesterday was 151.

Now, we can calculate the total revenue from selling these donuts using the given prices. We have:

Total revenue=(48×3.50)+(151×6.25)
Total revenue=168+943.75Total revenue=$1,111.75

Therefore, the store earned a total of $1,111.75 from selling 48 dozen glazed donuts and 151 dozen chocolate donuts yesterday.

This means that it is not possible that the store earned a total of $1,037.50 from selling 75 dozen glazed donuts and 124 dozen chocolate donuts yesterday, because these numbers do not satisfy the given conditions.