Answer :
Sure, let's solve this step-by-step. We need to fill in the missing values in the table by calculating the increase in value and the percentage increase.
Here’s the table with some provided values and formats for the solutions:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Original value} & \text{New Value} & \text{\begin{tabular}{c}
Increase in value \\ (Difference of new value \\ and original value)
\end{tabular}} & \text{\begin{tabular}{c}
Percentage Increase \\ (New Value - Original Value) / \\ Original Value \times 100\%
\end{tabular}} \\
\hline
20 & 25 & 5 & 25\% \\
\hline
210 & 283.5 & 73.5 & 35\% \\
\hline
80 & 100.8 & 20.8 & 26\% \\
\hline
260 & 293.8 & 33.8 & 13\% \\
\hline
568 & 1050.8 & 482.8 & 85\% \\
\hline
\end{array}
\][/tex]
Here's how we can calculate each missing value:
1. Row 1:
- Original value: 20
- New Value: 25
- Increase in value: [tex]\(25 - 20 = 5\)[/tex]
- Percentage Increase: [tex]\(\frac{5}{20} \times 100\% = 25\%\)[/tex]
2. Row 2:
- Original value: 210
- Percentage Increase: 35\% or 0.35 as a decimal
- Increase in value: [tex]\(210 \times 0.35 = 73.5\)[/tex]
- New Value: [tex]\(210 + 73.5 = 283.5\)[/tex]
3. Row 3:
- Original value: 80
- Percentage Increase: 26\% or 0.26 as a decimal
- Increase in value: [tex]\(80 \times 0.26 = 20.8\)[/tex]
- New Value: [tex]\(80 + 20.8 = 100.8\)[/tex]
4. Row 4:
- New Value: 293.8
- Increase in value: 33.8
- Original value: [tex]\(293.8 - 33.8 = 260\)[/tex]
- Percentage Increase: [tex]\(\frac{33.8}{260} \times 100\% \approx 13\%\)[/tex]
5. Row 5:
- New Value: 1050.8
- Increase in value: 482.8
- Original value: [tex]\(1050.8 - 482.8 = 568\)[/tex]
- Percentage Increase: [tex]\(\frac{482.8}{568} \times 100\% \approx 85\%\)[/tex]
So, here is the filled-in table with all the values calculated:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Original value} & \text{New Value} & \text{\begin{tabular}{c}
Increase in value \\ (Difference of new value \\ and original value)
\end{tabular}} & \text{\begin{tabular}{c}
Percentage Increase \\ (New Value - Original Value) / \\ Original Value \times 100\%
\end{tabular}} \\
\hline
20 & 25 & 5 & 25\% \\
\hline
210 & 283.5 & 73.5 & 35\% \\
\hline
80 & 100.8 & 20.8 & 26\% \\
\hline
260 & 293.8 & 33.8 & 13\% \\
\hline
568 & 1050.8 & 482.8 & 85\% \\
\hline
\end{array}
\][/tex]
Here’s the table with some provided values and formats for the solutions:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Original value} & \text{New Value} & \text{\begin{tabular}{c}
Increase in value \\ (Difference of new value \\ and original value)
\end{tabular}} & \text{\begin{tabular}{c}
Percentage Increase \\ (New Value - Original Value) / \\ Original Value \times 100\%
\end{tabular}} \\
\hline
20 & 25 & 5 & 25\% \\
\hline
210 & 283.5 & 73.5 & 35\% \\
\hline
80 & 100.8 & 20.8 & 26\% \\
\hline
260 & 293.8 & 33.8 & 13\% \\
\hline
568 & 1050.8 & 482.8 & 85\% \\
\hline
\end{array}
\][/tex]
Here's how we can calculate each missing value:
1. Row 1:
- Original value: 20
- New Value: 25
- Increase in value: [tex]\(25 - 20 = 5\)[/tex]
- Percentage Increase: [tex]\(\frac{5}{20} \times 100\% = 25\%\)[/tex]
2. Row 2:
- Original value: 210
- Percentage Increase: 35\% or 0.35 as a decimal
- Increase in value: [tex]\(210 \times 0.35 = 73.5\)[/tex]
- New Value: [tex]\(210 + 73.5 = 283.5\)[/tex]
3. Row 3:
- Original value: 80
- Percentage Increase: 26\% or 0.26 as a decimal
- Increase in value: [tex]\(80 \times 0.26 = 20.8\)[/tex]
- New Value: [tex]\(80 + 20.8 = 100.8\)[/tex]
4. Row 4:
- New Value: 293.8
- Increase in value: 33.8
- Original value: [tex]\(293.8 - 33.8 = 260\)[/tex]
- Percentage Increase: [tex]\(\frac{33.8}{260} \times 100\% \approx 13\%\)[/tex]
5. Row 5:
- New Value: 1050.8
- Increase in value: 482.8
- Original value: [tex]\(1050.8 - 482.8 = 568\)[/tex]
- Percentage Increase: [tex]\(\frac{482.8}{568} \times 100\% \approx 85\%\)[/tex]
So, here is the filled-in table with all the values calculated:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Original value} & \text{New Value} & \text{\begin{tabular}{c}
Increase in value \\ (Difference of new value \\ and original value)
\end{tabular}} & \text{\begin{tabular}{c}
Percentage Increase \\ (New Value - Original Value) / \\ Original Value \times 100\%
\end{tabular}} \\
\hline
20 & 25 & 5 & 25\% \\
\hline
210 & 283.5 & 73.5 & 35\% \\
\hline
80 & 100.8 & 20.8 & 26\% \\
\hline
260 & 293.8 & 33.8 & 13\% \\
\hline
568 & 1050.8 & 482.8 & 85\% \\
\hline
\end{array}
\][/tex]
