Please show me the formula you use.

Question

Profits on Nissan Altimas and Sentras average $1200 and $850. The total profits in one month in which they sold 120 of these models was $130,350. Find the number of each sold.

Answer 1

Let's use x to represent the number of Altimas sold, and y to represent the number of Sentras sold.

 

Then x + y = 120 because they sold 120 vehicles.

 

Now the profit on each Altima averaged $1200 and the profit on each Sentra averaged $850.  While they didn't make exactly those amounts on every car, because these are the averages, we can conclude that the profit on the Altimas was 1200x and the profit on the Sentras was 850y.  This is true because of the definition of an average.  For example

 

The average profit on Sentras = The sum of the profits on the x sentras divided by the number of sentras x, so if we then multiply the average by x we get the sum of the profit on Sentras back again.

 

So 1200x + 850y = 130,350 which is the total profit.

 

Now let's solve these two equations to find out the numbers of cars sold.

 

If we multiply both sides of the first equation by 850 we get

 

850x + 850y = 850*120

 

If we subtract this term-by-term from the second equation we get

 

350x = 130,350 - 850*120 = 28,350

 

So x = 81  - they sold 81 Altimas, and since x + y = 120,  y = 39 is the number of Sentras they sold.

 

 

 

  

Answer 2

Hi Bonnie

Let Pa=profit/car ($1,200/car) for Altimas and Ps=profit/ca($850/car) for Sentras. Na and Ns = the numbers sold during the month

 

We were told that PaxNa + PsxNs = 130,350 (total profit) and that Ns+Na=120 (number sold). So Ns=120-Na. If we substuite this in the first equation we get PaxNa + Psx(120-Na) = 130,350, solving this for Na gives Na=(130,350-120xPs)/(Pa-Ps)

 

or Na=81 cars and since Na+Ns=120 then Ns=120-Na or 39 cars. As a check using 81 and 39 in the total profit equation gives:

 

          1200x81 + 850x39 =130,350  which checks

So 81 Altimas and 39 Sentras were sold.

 

Hope this helps, let me know if you have any questions.

Jim