Advanced Algebra

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.
=========================
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.

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