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

Eliz.

#### Denis

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 ##### Elite Member 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

##### Senior Member
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