Contains X numbers, for what values of X

Question

for company A 

-the flat rate is $3.00 plus 7 cents per word

for company B

- the flat rate is $1.50 plus 12 cents per word 

Answer 1

Let P = price

Let W = number of words

 

The cost to use company A is P = 0.07*W + 3

The cost to use company B is P = 0.12*W + 1.5  

 

The 2 costs are equal when 

0.07*W + 3 = 0.12*W + 1.5

0.05*W = 1.5

W = 1.5 / 0.05 = 150/5 = 30 

 

So if you have less than 30 words then company B is cheaper

and if you have more than 30 words then company A is cheaper 

 

Check:  0.07*30 + 3 = 2.1 + 3 = $5.10

            0.12*30 + 1.5 = 3.6 + 1.5 = $5.10