Question

What number is increased by 1/4 of itself is equal to 30

Answer 1

We have the following case:

• We have a number and let this number be equal to x

• If this number is increased by 1/4 of itself, the number will be 30

And we have to find the value of the number x.

To find it, we can proceed as follows:

1. We can translate the situation into algebraic language as follows:

`x+(1)/(4)x=30`

When we say "increased by" we are adding a quantity to the original one.

2. And now, we can solve the equation as follows:

`\begin{gathered} x+(1)/(4)x=30 \\ \\ (4)/(4)x+(1)/(4)x=30 \\ \\ x((4+1)/(4))=30 \\ \\ x((5)/(4))=30\Rightarrow(5)/(4)x=30 \\ \end{gathered}`

3. Finally, we can multiply both sides by 4/5 as follows:

`\begin{gathered} (4)/(5)(5)/(4)x=(4)/(5)(30) \\ \\ x=4((30)/(5))=4(6)=24 \\ \\ x=24 \end{gathered}`

4. We can check this as follows:

`\begin{gathered} 24+(1)/(4)(24)=30 \\ \\ 24+6=30 \\ \\ 30=30 \end{gathered}`

Therefore, in summary, the number is 24 (x = 24).