MHB Mixing Teas for Profit: A 25% Return

  • Thread starter Thread starter splodge1
  • Start date Start date
  • Tags Tags
    Mixing
AI Thread Summary
A tea importer blends two types of tea, one costing £5.20/kg and the other £5.60/kg, selling the mix at £6.80/kg for a 25% profit. The calculations show that the cost price is £5.44, leading to the equation 5.2T1 + 5.6T2 = 5.44. By solving the equations, it is determined that the ratio of the less expensive tea (T1) to the more expensive tea (T2) is 2:3. This ratio indicates how the teas should be mixed for optimal profit. The discussion effectively demonstrates the mathematical approach to achieving a profitable tea blend.
splodge1
Messages
1
Reaction score
0
A tea importer mixes tea bought at £5.20/kg with tea at £5.60/kg. He sells this blend at £6.80/kg making a profit of 25% on his cost price. In what ratio does he mix the teas?
 
Mathematics news on Phys.org
Hello and welcome to MHB, splodge! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
Let's let $T_1$ be the amount of the less expensive tea in a kg of the mix and $T_2$ be the amount of the more expensive tea in a kg of the mix. So right away, we know:

$$T_1+T_2=1\tag{1}$$

Now, if the seller is making a 25% profit, then his cost is $$\frac{4}{5}$$ of the selling price, and so we may write:

$$5.2T_1+5.6T_2=0.8\cdot6.8=5.44$$

Multiplying through by 12.5, we have

$$65T_1+70T_2=68\tag{2}$$

Multiplying (1) by 65 and then subtracting it from (2), we get:

$$5T_2=3\implies T_2=\frac{3}{5}\implies T_1=\frac{2}{5}$$

And so we find:

$$T_1:T_2=2:3$$
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top