Question

The product of two numbers is 1296. If one number is 16 times the other, find the two numbers?

Answer 1

Hint: Here we have to first convert the statement to equation to solve it. Once the equation is solved we have to simplify it until we get the desired results.

Complete step-by-step answer:
As we are given with the product of two numbers is 1296. So, Let us assume the first number is x and the other number would be 16x as in the question it is clearly mentioned that the second number is 16 times of the first number.
Now we can write the equation as, \[x \times 16x = 1296\] .
Let us take x common in the left side of the equation, \[16{x^2} = 1296\] .
Let’s take 16 from left side to right side \[{x^2} = \dfrac{{1296}}{{16}}\] .
After dividing 1296 with 16 we get 81.
So, we get \[{x^2} = 81\] .
As we know that 81 is a square of 9.
So, we get \[{x^2} = {\left( 9 \right)^2}\] .
After calculating we can get to the final result that is \[x = 9\] .
First number is 9 and the second number is 16 times x.
\[16 \times x\] - equation 1.
Putting the value of x that is 9 in equation 1.
Now, we get \[16 \times x = 16 \times 9 = 144\]
Hence, the two numbers are 9 and 144.

Additional Information:
Many times we will see these types of questions where we have to convert statements into equations and start simplifying using BODMAS and then get the desired results.

Note: These types of questions can come in the form of H.C.F and L.C.M is given, and we have to calculate their product. We can use the formula that is a product of two numbers \[ = H.C.F \times L.C.M\] where L.C.M is least common multiple and H.C.F is highest common factor.