Question

Kevin is 39 years old and Daniel is 3 years old. How many years will it take until Kevin is only 4 times as old as Daniel ?

Answer 1

Hint:To solve the given question, read the question several times and note down all the key points and translate them into mathematical equations. Identify key phrases and organize the information by assigning variables (in form of letters) to the unknown quantities. Translate the problem into an algebraic equation using the phrases and variables and solve the equations using methods such as substitution, elimination etc, hence by this we can solve the sum.

Complete step by step answer:
Let us write the given data: Kevin = 39 years and Daniel = 3 years. And here we need to find the years for Kevin to be only 4 times as old as Daniel for this, let's create an equation to solve this problem. Let \[x\] represent the number of years that will need to pass. To represent Kevin's age, we'll use the expression \[39 + x\] and to represent 4 times Daniel's age, we'll use the expression \[4\left( {3 + x} \right)\].

In words, this equation can be represented as "Kevin's age plus \[x\] years is equal to four times Daniel's age plus \[x\] years." This is exactly what we need, since we need to know how many years will pass until Kevin's age is equal to four times Daniel's age.Since Daniel's age needs to be equal to 4 times Daniel's age, set the expressions equal to each other:
\[39 + x = 4\left( {3 + x} \right)\]
Now, let's expand and simplify this equation, start by applying the distributive property to the term \[4\left( {3 + x} \right)\].
\[\Rightarrow 4 \times 3 = 12\]
\[\Rightarrow 4 \times x = 4x\]
Inserting that back into the equation gives us:
\[39 + x = 12 + 4x\],
Now, let's move all of our x terms to one side, hence subtract x from each side as
\[39 = 12 + 3x\]
Let's get x by itself hence, Subtract 12 from both sides i.e.,
\[27 = 3x\]
Finally, divide both sides by three to get the value of x,
\[\therefore x = 9\].

Hence, it will take 9 years for Kevin to be only 4 times as old as Daniel.

Note:The key point to solve this sum is that we need to form equations by considering a variable, as we have taken \[x\] as a variable to find the age, next compare the data given with respect to the age of Kevin and Daniel, hence by comparing and solving the obtained equations we can get the value of \[x\] i.e., we have considered \[x\] as the age for Kevin to be only 4 times as old as Daniel.