Question 190: We're trying to solve the following linear function:
The price P of a soft drink is a linear function of the volune v of the cup. A 10-ounce drink sells for 50 cents and a 16-ounce drink sells for 68 cents. Write P as a linear function of v. What should the price be for a 20-ounce drink. Can you PLEASE help me solve this problem - I am at a complete loss. Thanks!
Beth
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
We're trying to solve the following linear function: The price P of a soft drink
is a linear function of the volune v of the cup. A 10-ounce drink sells for 50
cents and a 16-ounce drink sells for 68 cents. Write P as a linear function of v.<<
`
When v = 10, P = 50
When v = 16, P = 68
`
So the problem becomes
"Find the equation of a line which passes through the two points
(10,50) and (16,68)
` ` ` ` `y2 - y1
Use m = ---------, with (x1,y1) = (10,50) and (x2,y2) = (16,68)
` ` ` ` `x2 - x1
`
` ` ` ` ` 68-50 ` ` 18
` ` m = `------- = ---- = 3
` ` ` ` ` 16-10 ` ` `6
`
Now use y - y1 = m(x - x1)
` ` ` ` y - 50 = 3(x - 10)
` ` ` ` y - 50 = 3x - 30
` ` ` ` ` ` `y = 3x + 20
Now change x to v and y to P or P(v)
` ` ` ` ` ` `P = 3v + 20
or ` ` ` `P(v) = 3v + 20,
`
whichever form your teacher prefers.
`
>>What should the price be for a 20-ounce drink.<<
`
Substitute 20 for v:
` ` ` ` ` ` `P = 3v + 20 = 3(20) + 20 = 60 + 20 = 80 cents.
Edwin
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