Math Word Problem, Need Help

Question

The question says:

Caleb wants to ship a package to Alberta. He has two options:

I) Postal Express charges $6 plus 1 $ per kilogram.

II) Next day Delivery charges $2.50 per kilogram

a) Write an equation to model each Cost, C, in dollars, it relates to the number of kilograms.

_____________

I don't understand please help.

Answer 1

Postal Express costs C= 6 +K where K = number of kilograms

Next Day delivery: C=2.5K

the two cost the same $10, when 2.5K = 6+K

1.5K = 6

K=6/1.5 =4 kilograms

If the package weights more than 4 kilograms, it's cheaper to send send by Postal Express.

If you graph the two equations, they're both straight lines

measure kilograms on the x axis

measure cost on the y axis

Next Day delivery cost equation is a line through the origin,(0,0) with slope =2.5

Postal Express cost equation is a line with y intercept at 6 or the point (0,6) and a slope = 1. It's a 45 degree diagonal line. the 2.5 slope is steeper. The two lines intersect at (4,10) = (K,C)