The students are doing a fundraiser to help out a friend. They are selling chocolate and cookies for $3 and $2.50 respectively. The cookies were presold to 60 people. At least how many of the chocolates must be sold to collect $255?

At least 18 chocolates sold to collect $225

Step-by-step explanation:

~ Let's say x ⇒ the number of chocolates, y ⇒ the number of cookies ~

1. We can see that the number of chocolates/ cookies * the cost of chocolates/cookies = the total cost of chocolates/cookies. Provided this, it would be that 3x and 2.5y would represent the cost of chocolates and cookies.

2. It is given that there was $225 sold from chocolates and cookies, so we can say that 3x + 2.5y = 225 from this assumption.

3. That being said it is also known that the cookies were sold to 60 people, so we can assume that 60 cookies were sold out, 1 were person. With this information we can see that 3x ⇒ 3 * 60 = 180 ⇒ cost of cookies sold

4. Now we can substitute this value of 3x into the equation 3x + 2.5y = 225, as such: 3x + 2.5y = 225 ⇒ 180 + 2.5y = 225, and now we can solve for y ~

180 + 2.5y = 225,

2.5y = 225 - 180,

2.5y = 45,

y = 45/2.5,

y = At least 18 chocolates sold to collect $225

If you're studying differential equations, you can find the solution to the given equation using the boundary conditions given.

Some of us would rather cut to the chase. We recognize that this is an exponential decay problem in which the initial temperature difference from the 75 °F room temperature is decaying to zero.

In 10 minutes, the temperature difference has decayed from 180-75 = 105 to 100-75 = 25, so we can write the temperature function of time as
.. T(t) = 75 +105*(25/105)^(t/10)

We can solve this for
.. T(t) = 80
using logarithms, but it may be easier to do it graphically.

To the nearest minute, it will take 21 minutes for the coffee to cool to 80 °F.