Question

A number \[x\]is \[4\]less than three times another number \[y\]. If their sum is increased by \[5\], the result is \[25\]. Find both the numbers.

Answer 1

Hint: Two unknown numbers \[x\]and \[y\]are given in the question. It is also given that \[x\]is \[4\]less than three times another number \[y\], which means , and from other information, we will get that \[x + y + 5 = 25\]. By solving the two equations, we can get both the unknown numbers.

Complete step-by-step answer:
Let the first number be \[x\]and the second number be \[y\].
Given in the question, \[x\]is \[4\]less than three times another number \[y\]. When we write it in an equation, we can get:
\[ \Rightarrow x = 3y - 4\]
Similarly, it is given that, if their sum is increased by \[5\]then, the result will be \[25\]. So, we get:
\[ \Rightarrow x + y + 5 = 25\]
When we try to solve this, we get:
\[ \Rightarrow x + y = 25 - 5\]
\[ \Rightarrow x + y = 20\]
Hence, we get that \[x + y = 20\]
So, now we get two equations as:
\[x = 3y - 4\,\,\, ------ (eq1)\] and \[x + y = 20\,\, ----- (eq2)\].
Now putting the values of both the equations, we get:
\[ \Rightarrow 3y - 4 + y = 20\]
Now, we have to solve the equation, and we get:
\[ \Rightarrow 4y - 4 = 20\]
\[ \Rightarrow 4y = 20 + 4 = 24\]
\[ \Rightarrow y = \dfrac{{24}}{4}\]
\[ \Rightarrow y = 6\]
Now putting this value in \[(eq2)\],we get:
\[ \Rightarrow x + 6 = 20\]
\[ \Rightarrow x = 20 - 6\]
\[ \Rightarrow x = 14\]
Hence, \[x = 14\] and \[y = 6\].

Note: According to the question, the equations that we have solved here are Linear equations with two variables. The solution to these equations means finding the value of given variables which satisfies both the equations. Here we used the substitution method but as an alternate approach we could use the elimination method as well.