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Sagot :
To calculate Sarah's weekly allowance based on Plan A and Plan B, let's break down the approaches step-by-step.
### Plan A: Fixed Increase
In Plan A, Sarah's allowance increases by \[tex]$1 every week starting from \$[/tex]10.
### Plan B: Percentage Increase
In Plan B, Sarah's allowance increases by 10% every week starting from \[tex]$10. Step-by-step Calculation for Plan A: 1. Week 0: \$[/tex]10 (initial allowance)
2. Week 1: \[tex]$10 + \$[/tex]1 = \[tex]$11 3. Week 2: \$[/tex]11 + \[tex]$1 = \$[/tex]12
4. Week 3: \[tex]$12 + \$[/tex]1 = \[tex]$13 5. Week 4: \$[/tex]13 + \[tex]$1 = \$[/tex]14
6. Week 5: \[tex]$14 + \$[/tex]1 = \[tex]$15 7. Week 6: \$[/tex]15 + \[tex]$1 = \$[/tex]16
8. Week 7: \[tex]$16 + \$[/tex]1 = \[tex]$17 9. Week 8: \$[/tex]17 + \[tex]$1 = \$[/tex]18
10. Week 9: \[tex]$18 + \$[/tex]1 = \[tex]$19 11. Week 10: \$[/tex]19 + \[tex]$1 = \$[/tex]20
Plan A Summary:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Week} & & \text{Plan A} \\ \hline 0 & & \$10 \\ \hline 1 & & \$11 \\ \hline 2 & & \$12 \\ \hline 3 & & \$13 \\ \hline 4 & & \$14 \\ \hline 5 & & \$15 \\ \hline 6 & & \$16 \\ \hline 7 & & \$17 \\ \hline 8 & & \$18 \\ \hline 9 & & \$19 \\ \hline 10 & & \$20 \\ \hline \end{array} \][/tex]
Step-by-step Calculation for Plan B:
1. Week 0: \[tex]$10 (initial allowance) 2. Week 1: \$[/tex]10 \times 1.1 = \[tex]$11.00 3. Week 2: \$[/tex]11.00 \times 1.1 = \[tex]$12.10 4. Week 3: \$[/tex]12.10 \times 1.1 = \[tex]$13.31 5. Week 4: \$[/tex]13.31 \times 1.1 = \[tex]$14.64 6. Week 5: \$[/tex]14.64 \times 1.1 = \[tex]$16.10 7. Week 6: \$[/tex]16.10 \times 1.1 = \[tex]$17.72 8. Week 7: \$[/tex]17.72 \times 1.1 = \[tex]$19.49 9. Week 8: \$[/tex]19.49 \times 1.1 = \[tex]$21.44 10. Week 9: \$[/tex]21.44 \times 1.1 = \[tex]$23.58 11. Week 10: \$[/tex]23.58 \times 1.1 = \[tex]$25.94 Plan B Summary: \[ \begin{array}{|c|c|c|} \hline \text{Week} & & \text{Plan B} \\ \hline 0 & & \$[/tex]10.00 \\
\hline 1 & & \[tex]$11.00 \\ \hline 2 & & \$[/tex]12.10 \\
\hline 3 & & \[tex]$13.31 \\ \hline 4 & & \$[/tex]14.64 \\
\hline 5 & & \[tex]$16.10 \\ \hline 6 & & \$[/tex]17.72 \\
\hline 7 & & \[tex]$19.49 \\ \hline 8 & & \$[/tex]21.44 \\
\hline 9 & & \[tex]$23.58 \\ \hline 10 & & \$[/tex]25.94 \\
\hline
\end{array}
\]
By compiling these calculations, we can complete the table as follows:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Week} & & \text{Plan A} & \text{Plan B} \\ \hline 0 & & \$10.00 & \$10.00 \\ \hline 1 & & \$11.00 & \$11.00 \\ \hline 2 & & \$12.00 & \$12.10 \\ \hline 3 & & \$13.00 & \$13.31 \\ \hline 4 & & \$14.00 & \$14.64 \\ \hline 5 & & \$15.00 & \$16.10 \\ \hline 6 & & \$16.00 & \$17.72 \\ \hline 7 & & \$17.00 & \$19.49 \\ \hline 8 & & \$18.00 & \$21.44 \\ \hline 9 & & \$19.00 & \$23.58 \\ \hline 10 & & \$20.00 & \$25.94 \\ \hline \end{array} \][/tex]
This completed table shows the weekly allowance for Sarah under both plans over 10 weeks.
### Plan A: Fixed Increase
In Plan A, Sarah's allowance increases by \[tex]$1 every week starting from \$[/tex]10.
### Plan B: Percentage Increase
In Plan B, Sarah's allowance increases by 10% every week starting from \[tex]$10. Step-by-step Calculation for Plan A: 1. Week 0: \$[/tex]10 (initial allowance)
2. Week 1: \[tex]$10 + \$[/tex]1 = \[tex]$11 3. Week 2: \$[/tex]11 + \[tex]$1 = \$[/tex]12
4. Week 3: \[tex]$12 + \$[/tex]1 = \[tex]$13 5. Week 4: \$[/tex]13 + \[tex]$1 = \$[/tex]14
6. Week 5: \[tex]$14 + \$[/tex]1 = \[tex]$15 7. Week 6: \$[/tex]15 + \[tex]$1 = \$[/tex]16
8. Week 7: \[tex]$16 + \$[/tex]1 = \[tex]$17 9. Week 8: \$[/tex]17 + \[tex]$1 = \$[/tex]18
10. Week 9: \[tex]$18 + \$[/tex]1 = \[tex]$19 11. Week 10: \$[/tex]19 + \[tex]$1 = \$[/tex]20
Plan A Summary:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Week} & & \text{Plan A} \\ \hline 0 & & \$10 \\ \hline 1 & & \$11 \\ \hline 2 & & \$12 \\ \hline 3 & & \$13 \\ \hline 4 & & \$14 \\ \hline 5 & & \$15 \\ \hline 6 & & \$16 \\ \hline 7 & & \$17 \\ \hline 8 & & \$18 \\ \hline 9 & & \$19 \\ \hline 10 & & \$20 \\ \hline \end{array} \][/tex]
Step-by-step Calculation for Plan B:
1. Week 0: \[tex]$10 (initial allowance) 2. Week 1: \$[/tex]10 \times 1.1 = \[tex]$11.00 3. Week 2: \$[/tex]11.00 \times 1.1 = \[tex]$12.10 4. Week 3: \$[/tex]12.10 \times 1.1 = \[tex]$13.31 5. Week 4: \$[/tex]13.31 \times 1.1 = \[tex]$14.64 6. Week 5: \$[/tex]14.64 \times 1.1 = \[tex]$16.10 7. Week 6: \$[/tex]16.10 \times 1.1 = \[tex]$17.72 8. Week 7: \$[/tex]17.72 \times 1.1 = \[tex]$19.49 9. Week 8: \$[/tex]19.49 \times 1.1 = \[tex]$21.44 10. Week 9: \$[/tex]21.44 \times 1.1 = \[tex]$23.58 11. Week 10: \$[/tex]23.58 \times 1.1 = \[tex]$25.94 Plan B Summary: \[ \begin{array}{|c|c|c|} \hline \text{Week} & & \text{Plan B} \\ \hline 0 & & \$[/tex]10.00 \\
\hline 1 & & \[tex]$11.00 \\ \hline 2 & & \$[/tex]12.10 \\
\hline 3 & & \[tex]$13.31 \\ \hline 4 & & \$[/tex]14.64 \\
\hline 5 & & \[tex]$16.10 \\ \hline 6 & & \$[/tex]17.72 \\
\hline 7 & & \[tex]$19.49 \\ \hline 8 & & \$[/tex]21.44 \\
\hline 9 & & \[tex]$23.58 \\ \hline 10 & & \$[/tex]25.94 \\
\hline
\end{array}
\]
By compiling these calculations, we can complete the table as follows:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Week} & & \text{Plan A} & \text{Plan B} \\ \hline 0 & & \$10.00 & \$10.00 \\ \hline 1 & & \$11.00 & \$11.00 \\ \hline 2 & & \$12.00 & \$12.10 \\ \hline 3 & & \$13.00 & \$13.31 \\ \hline 4 & & \$14.00 & \$14.64 \\ \hline 5 & & \$15.00 & \$16.10 \\ \hline 6 & & \$16.00 & \$17.72 \\ \hline 7 & & \$17.00 & \$19.49 \\ \hline 8 & & \$18.00 & \$21.44 \\ \hline 9 & & \$19.00 & \$23.58 \\ \hline 10 & & \$20.00 & \$25.94 \\ \hline \end{array} \][/tex]
This completed table shows the weekly allowance for Sarah under both plans over 10 weeks.
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