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Question 161513This question is from textbook ELEMENTARY AND INTERMEDIATE ALGEBRA
: A 10-ounce soft drink sells for 50 cents, and a 16-ounce
soft drink sells for 68 cents. The price P is determined
from the volume v of the cup by a linear equation.
a) Find the equation.
b) Find the price of a 20-ounce soft drink.
This question is from textbook ELEMENTARY AND INTERMEDIATE ALGEBRA
Found 2 solutions by scott8148, gonzo:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! a) 6 more ounces (16-10) cost 18 more cents (68-50) __ so the drink costs 3 cents per ounce (18/6)
P=3v+k __ 50=3(10)+k __ 20=k __ k might represent the cost of the cup plus labor
P=3v+20
b) P=3(20)+20 __ P=80
Answer by gonzo(654)  (Show Source):
You can put this solution on YOUR website! x = ounces
y = price
slope intercept form of the equation is
y = m*x + b
you need 2 point on the graph to find the slope.
one of the points is (10,50)
the other point is (16,68)
slope is determined by the formula
(y-y1)/(x-x1)
let (x,y) = (16,68)
let (x1,y1) = (10,50)
slope is then
(68-50)/(16-10) = 18/6 = 3
slope intercept form of the equation becomes
y = 3*x + b
to solve for b, use one of the points.
take (x1,y1) = (10,50)
equation becomes
50 = 3*(10) + b
which becomes
50 = 30 + b
subtract 30 from both sides of equation to get
50 - 30 = b
which becomes
20 = b
slope intercept form of the equation is now
y = 3*x + 20
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to prove this is good, substitute the known points in the equation.
first use (10,50)
equation becomes
50 = 3*(10) + 20
50 = 30 + 20
50 = 50
equation is good for first set of points.
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next use (16,68)
equation becomes
68 = 3*(16) + 20
68 = 48 + 20
68 = 68
equation is good for the second set of points.
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equation is
y = 3*x + 20
use the equation to solve for when x = 20.
substitute 20 for x and the equation becomes
y = 3*(20) + 20
this becomes
y = 60 + 20
which becomes
y = 80
price for a 20 ounce soda would be 80 cents.
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graph of the equation should show that when x = 20, y = 80
graph of the equation is shown below.
x axis represents ounces of soda.
y axis represents cost of soda in cents.
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