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!
R means lbs regular, A means lbs all spice
cost ingredients= cost mix
R*.9 + A*1.20=(R+A)1.65(2/3)
solve for R/A
Notice the 2/3. If the selling price is 1.65, then 2/3 of that must be cost. (1/3 is profit).
Rebecca,
There is another way (but much much much longer) of doing this.
R = weight of regular tea.
A = weight of spiced tea.
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If we make a 100 lb sample then
R + A = 100. This is equation 1.
The cost will be 0.90R + 1.20A and we want a 50% profit.
The selling price is 1.65(R + A).
Remember [(selling price - cost)/cost] x 100 = 50%
Then {[1.65(R + A) -(0.90R + 1.20A)]/(0.90R + 1.20A)}= 0.5
This is equation 2.
Solve the two equations for R and A, then take the ratio of R to A. If you want to go through it check out my figures. I arrived at 33.33 lbs for R and 66.67 lbs for A which is a ratio of 33.33/66.67 = 1R/2A. I hope this helps.
To solve this problem, we need to set up a system of equations.
Let's say the weight of regular tea is R lbs and the weight of all-spice tea is A lbs.
According to the information given, the cost of regular tea is $0.90 per pound and the cost of all-spice tea is $1.20 per pound.
The cost of the ingredients in the mixture is given by:
Cost of regular tea + Cost of all-spice tea = Cost of the mixture
(R * 0.90) + (A * 1.20) = (R + A) * 1.65
To achieve a 50% profit over the wholesale cost, we can calculate the cost of the mixture as 2/3 of the selling price:
Cost of the mixture = (2/3) * Selling price
Substituting in the given selling price of $1.65 per pound, we have:
(R * 0.90) + (A * 1.20) = (R + A) * 1.65 * (2/3)
Simplifying this equation, we get:
0.9R + 1.2A = 1.1R + 1.1A
Rearranging terms, we have:
0.2R = 0.1A
Dividing both sides of the equation by A, we get:
R/A = 0.1/0.2
Simplifying this ratio, we have:
R/A = 1/2
Therefore, the ratio of regular tea to all-spice tea should be 1:2 to accomplish a 50% profit over the wholesale cost.