Video Transcript
A company produces lollipops. In the equations 𝐶 of 𝑥 equals
3000 plus three-halves 𝑥, 𝑅 of 𝑥 equals two 𝑥, the function 𝐶 of 𝑥 represents
the total production cost, in dollars, of 𝑥 lollipops. And the function 𝑅 of 𝑥
represents the total revenue, in dollars, from selling 𝑥 lollipops. How many lollipops should be
produced so that the total cost of production is equal to the total revenue gained
from selling them?
We know that 𝐶 of 𝑥 is our
production cost. And 𝑅 of 𝑥 is our revenue. We’re looking for the place where
these two values are equal. 3000 plus three-halves 𝑥 equals
two 𝑥, production equal to revenue. At this point, we want to solve for
𝑥, which will tell us how many lollipops need to be produced so that these two
equations are equal. First, subtract three-halves 𝑥
from both sides of the equation. I know that two is equal to four
over two. And four over two minus three over
two equals one-half. So we have one-half 𝑥
remaining. Two minus three-halves or two minus
one and a half is equal to one-half. And we have the variable 𝑥.
Now, if one-half 𝑥 equals 3000, we
can multiply both sides of the equation to find out how much 𝑥 is equal to. One-half 𝑥 times two equals
𝑥. And two times 3000 equals 6000. This means that when the company
produces 6000 lollipops, the cost of production is equal to the revenue gained from
selling the same amount. We can check that this is true. First with the production cost,
3000 plus three-halves times 6000 equals 12000 dollars. That’s how much it costs to produce
6000 lollipops. And we multiply two times 6000 to
get the total revenue from selling 6000 lollipops. Two times 6000 is 12000, which
confirms what we found.
