Question

The school band sells carnations on Valentine’s Day for $3 each. It buys the carnations from a florist for $0.50 each, plus a $18 delivery charge. When will the cost of the carnations be equal to the revenue from selling them? How many carnations does it need to sell to reach this point?

Answer 1

To reach the point where the cost of the carnations is equal to the revenue from selling them, the school band needs to sell at least 8 carnations.

Step-by-step explanation:

To find when the cost of the carnations will be equal to the revenue from selling them, we need to set up an equation. Let x be the number of carnations sold. The cost of buying x carnations is given by 0.50x + 18, and the revenue from selling x carnations is given by 3x. So, we set up the equation:

0.50x + 18 = 3x

Solving for x, we get:

18 = 2.50x

x = 18 / 2.50

x = 7.2

Since we can't sell a fraction of a carnation, we round up to the nearest whole number. Therefore, the school band needs to sell at least 8 carnations to reach the point where the cost of the carnations is equal to the revenue from selling them.

Answer 2

Let's denote the number of carnations as x. We can express the revenue as
`3x` and the cost as
`0.50x+18`.

To find when the cost and revenue will be equal, we just equate the two expressions. We need to solve for x to find the number of carnations needed to reach that point.


`3x=0.50x+18`

`2.50x=18`

`x=7.2`

For the revenue to be equal, the number of carnations sold should be equal to 7.2, BUT, realistically speaking, we can never have 0.2 of a carnation. So, the cost of the carnations will NEVER equal the revenue of selling them. 7 carnations sold would have a slightly smaller revenue compared to the cost and 8 carnations sold would have a larger revenue.