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?

Question

anonymous · Answer

hey guys

anonymous · Answer

i need help

mathmale · Answer

Hey, goel, what have you been able to do so far towards solving this problem?

anonymous · Answer

.... nothing
im in an advanced class and dont know to do this

mathmale · Answer

This problem is a bit harder than those I'm used to in that we don't know the constraints on x and y, other that x and y must both be positive.  Generally, we're told that we need to make P pounds of mixture selling at $1.65 per pound, which is a constraint:  x + y = P.
Here we don't have the luxury of having that info, at least not explicitly.  Does this ring a bell at all?  We need to figure out how to include a 50% profit into our calculations.

mathmale · Answer

In general, profit = Total selling price - (Total purchase price and costs).

anonymous · Answer

im confused

mathmale · Answer

"I'm confused" is a natural response.  But I'm hoping you can turn your confusion into some good questions that might lead us to a solution.  What do YOU think we need to know to solve this problem?  I've already given you one hint:  the selling price needs to be 50% higher than the price the seller pays wholesale for these two teas.

mathmale · Answer

@cgoel:  we do need to choose at least 2 different variables to represent the unknowns here.  What unknowns are we discussing here?

mathmale · Answer

Let x = the number of (?) of (  ?  )
Let y = the number of (?) of (  ?  )

mertsj · Answer

1.65(x+y)=1.5(.9x+1.2y)
1.65x+1.65y=1.35x+1.8y
.30x=.15y
x/y=.15/.30
x/y=1/2

mathmale · Answer

@cgoel:  Mertsj has done a great job here of setting up a relationship between x and y.  His 1.5 includes the 50% markup on wholesale.  His (x+y) denotes the total number of pounds of the tea mixture.  He recognizes that we do not need to find x and y, but only their ratio.  His result, x/y = 1/2, tells us that the number of pounds of the cheaper tea should be 1/2 of the number of pounds of the more expensive tea.  I ask that you read through this and ask questions about whatever remains unclear to you.

anonymous · Answer

thank you guys!

mathmale · Answer

"What should the ratio of regular to all-spice be to accomplish this?"

mathmale · Answer

"Ratio" is the key word here.