Word Problem: Mr Whipple wants to blend two teas....

megan0430

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Aug 23, 2006
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Mr. Whipple wants to blend two teas, regular and all-spice, whose wholesale cost is $0.90/lb and $1.20/lb respectively. He wil sell the mixture at $1.65/lb and wishes to make a 50% profit over wholesale cost. What should the ratio of regular to all-spice be to accomplish this?

PLEASE HELP.
THANKS!
 

stapel

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First step: If the sale price is to be $1.65 per pound, and if this is to be a fifty-percent mark-up on cost, what should be the cost per pound?

Please reply showing how far you have gotten. Thank you.

Eliz.
 

Denis

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megan0430 said:
Mr. Whipple wants to blend two teas, regular and all-spice, whose wholesale cost is $0.90/lb and $1.20/lb respectively. He wil sell the mixture at $1.65/lb and wishes to make a 50% profit over wholesale cost. What should the ratio of regular to all-spice be to accomplish this?
selling prices:
regular: .90 * 1.5 = 1.35
all-spice: 1.20 * 1.5 = 1.80

Now you need to find the combination of these 2 prices that results in 1.65
 

soroban

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Hello, Megan!

I thought this was a basic "Mixture Problem"
. . but there was more to it.


Mr. Whipple wants to blend two teas, regular and all-spice,
whose wholesale cost is $0.90/lb and $1.20/lb respectively.
He wil sell the mixture at $1.65/lb and wishes to make a 50% profit over wholesale cost.
What should the ratio of regular to all-spice be to accomplish this?

To make a 50% profit when selling at $1.65/lb, the cost must have been $1.10/lb.
Now we are back to a basic Mixture Problem.

He will use \(\displaystyle R\) pounds of regular tea and \(\displaystyle S\) pounds of spiced tea.

The \(\displaystyle R\) pounds of regular tea costs $0.90/lb: the value is \(\displaystyle \L0.90R\) dollars.

The \(\displaystyle S\) pounds of spiced tea costs $1.20/lb; the value is \(\displaystyle \L1.20S\) dollars.

The total of \(\displaystyle R+S\) pounds of tea cost $1.10/lb; the value is \(\displaystyle \L1.10(R+S)\) dollars.

And there is our equation: \(\displaystyle \L\,0.90R\,+\,1.20S\:=\:1.10(R\,+\,S)\)


Multiply by 10: \(\displaystyle \L\:9R\,+\,12S\:=\:11(R\,+\,S)\;\;\Rightarrow\;\;9R\,+\,12S\:=\:11R\,+\,11S\)

\(\displaystyle \;\;\)and we have: \(\displaystyle \L\:2R\:=\:S\;\;\Rightarrow\;\;\frac{R}{S}\:=\:\frac{1}{2}\)

Therefore, the ratio of regular to spiced tea is 1:2

 

Denis

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Feb 17, 2004
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selling prices:
regular: .90 * 1.5 = 1.35
all-spice: 1.20 * 1.5 = 1.80

Further to above; use 1 pound:

r @ 1.35
1-r @ 1.80
------------
1 @ 1.65

1.35r + 1.80(1-r) = 1.65
1.35r + 1.80 - 1.80r = 1.65
.45r = .15
r = .15/.45 = 1/3 ; so allspice = 2/3; so 1:2
 
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