Question

If 200 is increased by 12 1/4 percent, what is the resulting number?

Answer 1

`\text{resulting number= }224.5`

Step-by-step explanation

Step 1

convert the mixed number into a fraction number.

remember:

`a\text{ }(b)/(c)=((a\cdot c)+b)/(c)`

hence

`12(1)/(4)=((12\cdot4)+1)/(4)=(48+1)/(4)=(49)/(4)`

Step 2

now, use a rule of three to find the increase in 49/4 percet

so, find the increase

`\begin{gathered} \text{if} \\ 200\Rightarrow100 \\ x\Rightarrow(49)/(4) \end{gathered}`

do the proportion and solve for x

`\begin{gathered} (200)/(100)=(x)/((49)/(4)) \\ \text{cross multiply} \\ 200\cdot(49)/(4)=100x \\ 2450=100x \\ \text{divide both sides by 100} \\ (2450)/(100)=(100x)/(100) \\ 24.5=x \end{gathered}`

so, the increase is 24.5

Step 3

finally, add the increase to the 200 to know the resulting number

`\begin{gathered} \text{resulting number= 200+24.5} \\ \text{resulting number= }224.5 \end{gathered}`

I hope this helps you