SOLUTION: A bakery sells cheesecakes having diameters 6 in, 8 in, 10 in; all the same height. Suppose that they cost $8, $12, and $20 respectively.
A. Which size gives you the most cheese
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Question 171926: A bakery sells cheesecakes having diameters 6 in, 8 in, 10 in; all the same height. Suppose that they cost $8, $12, and $20 respectively.
A. Which size gives you the most cheesecake per dollar?
please explain.
B. Find a quadratic equation that models how the ocst of a cheesecake varies with diameter.
I would appreciate any help I can get.
Please help soon!
Found 2 solutions by Mathtut, stanbon:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
A.
6in=sq inches
8in =sq inches
10in=sq. inches
:
price per sq in:
:
6in per sq in
8in per sq in
10inper sq in
:
inch pie gives you the most bang for your buck
:
B. let T be total cost of pie, C= cost / sq in
:
.......where r is the radius of the pie
:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A bakery sells cheesecakes having diameters 6 in, 8 in, 10 in; all the same height. Suppose that they cost $8, $12, and $20 respectively.
A. Which size gives you the most cheesecake per dollar?
please explain.
---
The volume of each pie is (pi)r^2h; pi and h are the same for each pie
so the volume depends on r^2 for each pie
-----------
The 6" has r^2 = 9 and the cost is (9/8)pih = 1.125 pih/dollar
The 8" has r^2 = 16 and the cost is (16/12)pih = 1.3333..pih/dollar
The 10" has r^2 = 25 and the cost is (25/20pih = 1.25 pih/dollar
--------------------------
So the best buy is the 8" pie which gives you more volume per dollar
============================================================================
B. Find a quadratic equation that models how the cost of a cheesecake varies
You have three points: (6,8), (8,12), (10,20)
The quadratic form is ax^2 + bx + c = y
Substitute to get three equations in a,b, and c
--------------------------------------------------
36a + 6b + c = 8
64a + 8b + c = 12
100a + 10b +c = 20
----------------------
Solve by any method you know to get:
a = 1/2
b = -5
c = 20
-----------------
Equations:
y = (1/2)x^2 -5x + 20
===========================
Cheers,
Stan H.
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