Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
