Sugars

In what ratio must two sorts of sugar, costing #390 and #315 per kg respectively, be mixed in order to produce a mixture worth #369 per kg?

Correct answer:

r =  18:7

Step-by-step explanation:

$$\begin{gathered} b=1 \\ 390a+315b=369(a+b) \\ 390\cdot a+315\cdot 1=369\cdot (a+1) \\ 21a=54 \\ a={\displaystyle \frac{18}{7}}\doteq 2.571429 \\ r=a\mathrm{/}b=2.5714\mathrm{/}1={\displaystyle \frac{18}{7}}=2\frac{4}{7}\approx 2.5714=18:7 \end{gathered}$$

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