Hi Chantilly. Tho start this problem, we should look for the most basic equation to describe the plant first. We are looking for an equation for the number of cars produced, knowing that they plant started with an initial inventory and that new cars are produced at a steady rate. From this, we can write the very generic equation:
CT = CI + rd Equation 1
where CT= total number of cars, CI= the initial inventory, r= rate of production/day and d= number of days that have past.
We know from the above that CI and r will have numerical values, which we must solve for and d will be our variable. We must then find the values for CI and r.
Let's start with the value for r. We are told that three days ago, we have 450 cars and yesterday (two days later) we have 480 cars. The difference in these numbers will give us how many cars were produced in two days. 480-450= 30 new cars in two days. Since r is the rate of production/day, and we know that 30 cars were produced in two days, we can find the rate/day by dividing 30 new cars by 2 days to get 15 cars produced/day. r = 15 cars/day.
Now we can rewrite the original equation with this new rate plugged in for r :
CT = CI + 15d Equation 2
Next, we must solve for CI. We are told two pieces of information that will help us solve for this variable. First, the plant was opened 25 days ago. Second, that yesterday (24 days after the plant opened), there were 480 cars in inventory. We can plug these numbers in the equation above and then solve for CI
480 = CI + (15x24)
After you solve for CI, you can plug that number into Equation 2 and you have your final equation.