PLEASE HELP.

THANKS!

- Thread starter megan0430
- Start date

PLEASE HELP.

THANKS!

selling prices: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?

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

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

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

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