From health tips to tech hacks, find it all on IDNLearn.com. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.
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.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.