# SOLUTION: 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

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: 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       Log On

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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 ----- 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. ----- next use (16,68) equation becomes 68 = 3*(16) + 20 68 = 48 + 20 68 = 68 equation is good for the second set of points. ----- 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. ----- 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.