Mixture of nuts

Alice bought a mixture of nuts containing cashew nuts, hazelnuts, and peanuts in a ratio of 1:2:3. If the peanuts weigh 90 g, calculate the weight in grams of the whole mixture.

Correct answer:

x =  180 g

Step-by-step explanation:

$$\begin{gathered} \frac{3}{1+2+3}\cdot x=90 \\ x=90/\frac{3}{1+2+3}=180=180\text{g} \\ \text{ Verifying Solution: } \\ k=x\cdot \frac{1}{1+2+3}=180\cdot \frac{1}{1+2+3}=30\text{g} \\ l=x\cdot \frac{2}{1+2+3}=180\cdot \frac{2}{1+2+3}=60\text{g} \\ m=k+l+90=30+60+90=180 \\ m=x \end{gathered}$$

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