Question

Solve the following riddle:
I am a number, tell my identity!
Take me seven times over, And add a fifty!
To reach a triple century, You still need forty!

Answer 1

Hint: In order to find the solution to this question, we will first consider the number as x and then by the given conditions we will try to form a linear equation in one variable. To get started, we have to decode “Take me seven times over” as adding x 7 times, i.e 7x. Then, we have to go word by word and decode each condition. As we have been asked to calculate the number, we will simplify the obtained equation and get the value of x to get out the answer.

Complete step-by-step answer:
In this question, we have been given a riddle and we have been asked to find the number. So, to solve this question, we will first consider the number as x and then we will form the linear equation in one variable.
Now, we have been given that the number is taken up to seven times. So, we can say the number added with itself up to seven times, so we have 7x now. And then we have been given that 50 is added with the obtained number, so it becomes 7x+50. Then we still need forty to reach a triple century. So, it means that the number 7x+50 is the same as (3 times 100) - 40.
So, we can say that the given riddle will look like,
\[7x+50=3\left( 100 \right)-40\]
Now, we will simplify it to get the value of x. So, we get,
\[7x+50=300-40\]
And we know that only like terms show the addition and subtraction. Therefore, we get,
\[7x=260-50\]
And it can be further written as,
\[7x=210\]
Now, we will divide both sides of the equation by 7. Therefore, we get,
\[\dfrac{7x}{7}=\dfrac{210}{7}\]
Now, we know that the common terms of the numerator and denominator get canceled out. Therefore, we get, x = 30.
Hence, we get the number as 30. Therefore, we can say that 30 is the number which is taken seven times and 50 is added to them, such that it still requires forty to reach the triple century.

Note: While forming the equation, we can also use the concept that 7x+50 needs an additional 40 to be added to it to reach triple century. So, we can write the equation as 7x+50+40=3(100). While solving this question, the possible mistake one can make is not making the appropriate linear equation from the given information by writing 7x as 7 + x or \[{{x}^{7}}\] or something else which will give us the wrong answer in a hurry. So, we have to be very careful while solving.