Question

Bella and Edward have different Math Teachers. Bella said to Edward, "O have more of my homework done than you. I did eighteen out of thirty-six problems so far." Edward disagrees saying "No way! I already did ____ out of forty-eight! What was the least number of problems that Edward must have done to have completed a greater percentage of his assigned homework than Bella?

Answer 1

Explanation

Step1

find the percent of Bella

$\text{percentage=}\frac{Number\text{ of done problems}}{\text{Total of problems}}\cdot100$

$\begin{gathered} \frac{18}{36}=\frac{1}{2}=0.5 \\ 0.5\cdot100\rightarrow50\text{ per cent} \end{gathered}$

so, the percentage of done homework for Bella is 50 %

Step 2

Let x represents the number of problems Edward has done

then

$\begin{gathered} \text{percentage=}\frac{Number\text{ of done problems}}{\text{Total of problems}}\cdot100 \\ \text{percentage=}\frac{x}{\text{4}9}\cdot100 \\ \frac{100x}{49} \end{gathered}$

Hence

$\begin{gathered} \frac{100x}{49}\text{ must be gretar than 50 per cent} \\ \frac{100x}{49}\text{ }>50 \\ \text{now, solve} \\ \text{Multiply both sides by 49} \\ \frac{100x}{49}\cdot49>50\cdot49 \\ 100x>2450 \\ \text{divide both sides by 100} \\ \frac{100x}{100}>\frac{2450}{100} \\ x>24.5 \\ we\text{ n}eed\text{ a integer number ( then round the number)} \\ x>25 \end{gathered}$

I hope this helps you