Question

One year ago, Clare was \[4\] feet $6$ inches tall. Now Clare is $4$ feet $10$ inches tall. By what percentage did Clare’s height increase in the last year?

Answer 1

Hint: In the given question, we are given that one year ago, Clare was \[4\] feet $6$ inches tall, now she is $4$ feet $10$ inches tall and we need to find by what percentage did Clare’s height increase in the last year. The percentage change is defined as the difference between the initial value and the final value of a quantity expressed in a percentage. First, we will convert the height into the same measurement. After this, using the percentage increase formula we will find the percentage increase in height.
Formula used: \[{\text{Percentage Increase = }}\dfrac{{Final{\text{ }}Value - Initial{\text{ }}Value}}{{\left| {Initial{\text{ }}Value} \right|}} \times 100\]

Complete step by step answer:
Given,
Initial value = \[4\] feet $6$ inches
Final value = \[4\] feet $10$ inches
At first, we will convert the inches into its equivalent value in units of feet using the unit conversion, $1foot = 12inches$.
\[4\] feet $6$ inches = $4foot + \left( {6inches \times \dfrac{{1foot}}{{12inches}}} \right) = 4.5feet$
\[4\] feet $10$ inches = $4foot + \left( {10inches \times \dfrac{{1foot}}{{12inches}}} \right) = 4.8333feet$
Now, we will substitute the values in the percentage increase formula,
\[{\text{Percentage Increase = }}\dfrac{{4.8333 - 4.5}}{{\left| {4.5} \right|}} \times 100\]
On subtraction of terms, we get
\[{\text{Percentage Increase = }}\dfrac{{0.3333}}{{4.5}} \times 100\]
On solving, we get
\[{\text{Percentage Increase = 7}}{\text{.40666% }}\]
On rounding off, we get
\[{\text{Percentage Increase = 7}}{\text{.41% }}\]
Therefore, Clare’s height increased by $7.41\% $ in the last year.

Note:
To solve this type of question, always remember to first convert the height in the same measurement. Here, we converted $6$ inches into feet by dividing it by $12$. We can also solve the given question by converting $4$ feet into inches, by multiplying it by $12$. We should take care of the calculations so as to be sure of our final answer. Remember to write units.