Three-fourths 5676

The three numbers are in the ratio of 4:7:14. Three-fourths of the smallest number is one greater than one-fifth of the largest number. How many times is the product of these three numbers greater than their sum?

Correct answer:

x =  392

Step-by-step explanation:

$$\begin{gathered} a=4k \\ b=7k \\ c=14k \\ 3/4a=1+c/5 \\ 3/4\cdot 4k=1+14k/5 \\ k=1/(3-14/5)=5 \\ a=4\cdot k=4\cdot 5=20 \\ b=7\cdot k=7\cdot 5=35 \\ c=14\cdot k=14\cdot 5=70 \\ x=a\cdot b\cdot c/(a+b+c)=20\cdot 35\cdot 70/(20+35+70)=392 \end{gathered}$$

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