systems of equations

Question

A company manufactures decorative flags and wants to determine the number of flags n to produce (break point) that will cost equal amounts using either of their two machines, Brand A and Brand B. Brand A machine costs $600 and $5 per flag to produce. Brand B machine costs $1,000 and $3 per flag to produce. Find the break point n. (Enter an exact number.)

 

n=________

Answer 1

So, the trick is to put total cost on one side of the equation and total number of flags on the other.

 

Let "n" be the number of flags

 

600 = 5n would yield an n of 120

 

1000 = 3n would yield an n of 333.

 

The key is to combine the equations 

 

600 + 1000 = 1600 = 5n + 3n = 8n

 

So, n = 1600 / 8 = 200.

 

Notice an n of 200 times 5 equals the $1000 cost of Brand B, which also surpasses the value of Brand A.