SOLUTION: I'm not sure how to do the following word problem: A 10 ounce box of bran flakes costs $3 and a 15 ounce box of the same bran flakes $4. Write a linear function that describes th

Algebra ->  Functions -> SOLUTION: I'm not sure how to do the following word problem: A 10 ounce box of bran flakes costs $3 and a 15 ounce box of the same bran flakes $4. Write a linear function that describes th      Log On


   

Question 818906: I'm not sure how to do the following word problem:
A 10 ounce box of bran flakes costs $3 and a 15 ounce box of the same bran flakes $4. Write a linear function that describes the cost of a box of bran flakes as a function of its weight and find the cost of the box. Assume both size boxes cost the same.
Thank you!
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
The given information only allows to find the price versus box size. You can also find the price per ounce of bran flakes.
(size, price) as points using variables, (x,p) where p is price and x is size.

The two data points are (10,3) and (15,4). Fit to a line equation.
slope is %284-3%29%2F%2815-10%29=1%2F5
p=%281%2F5%29x%2Bb
b=p-%281%2F5%29x
Pick any point to find b.
b=3-%281%2F5%2910
b=3-2
b=1
EQUATION: highlight%28p=%281%2F5%29x%2B1%29

A box size for 0 ounces costs 1 dollar. According to the slope, each ounce of blan flakes is (1/5) of a dollar or 0.20 dollars. This function p(x) still indicates 1 dollar to be added to this. If a box were made to hold 5 ounces, then the price for this box would be p=%281%2F5%295%2B1=highlight%282%29 dollars.