Question

Three numbers aren’t known, but the ratio of the numbers is$1:2:5$ . Is it possible that the numbers are$1,2,$ and5.$10,20,$ and$50?$$3,6,$ and$20?$ $x,2x,$and$5x?$

Short answer

The answer is $(1,2,5),(10,20,50)$and $(x,2x,5x)$.

Step-by-step solution

Step 1. Given information.

Ratio of three unknown numbers is$1:2:5$.

numbers can be$1,2\text{\hspace{0.17em}and5\hspace{0.17em}or}10,20\text{\hspace{0.17em}and50\hspace{0.17em}or\hspace{0.17em}3},6\text{\hspace{0.17em}and20\hspace{0.17em}or\hspace{0.17em}}x,2x\text{\hspace{0.17em}and5}x$.

Ratio is$1:2:5$ .

Step 2. Checking first pair of numbers.

$1:2:5$, this is possible.

Step 3. Checking second pair of numbers.

$\begin{array}{l}10:20:50\\ \text{Dividingby10}\\ 1:2:5\end{array}$

These numbers are also possible.

Step 4. Checking third pair of numbers.

$3:6:20$

Not possible.

Step 5. Checking fourth pair of numbers.

$\begin{array}{l}x:2x:5x\\ \text{Dividingby}x\\ 1:2:5\end{array}$

Therese numbers are possible.

Therefore, the answer is$(1,2,5),(10,20,50)$ and$(x,2x,5x)$ .