Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's solve the problem step-by-step.
1. Define Variables:
- Let [tex]\( x \)[/tex] represent the amount of money Deon has.
2. Express Christine's and Alan's Amounts in Terms of [tex]\( x \)[/tex]:
- Christine has [tex]$9 more than Deon. Thus, Christine has \( x + 9 \) dollars. - Alan has 4 times what Deon has. Hence, Alan has \( 4x \) dollars. 3. Set Up the Equation: - The total amount of money they have is $[/tex]99.
- Therefore, we can set up the following equation:
[tex]\[ x (Deon) + (x + 9) (Christine) + (4x) (Alan) = 99 \][/tex]
4. Combine Like Terms:
[tex]\[ x + x + 9 + 4x = 99 \][/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 6x + 9 = 99 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Subtract 9 from both sides:
[tex]\[ 6x = 90 \][/tex]
- Divide by 6:
[tex]\[ x = 15 \][/tex]
- Thus, Deon has [tex]$15. 6. Calculate Christine's Amount: - Christine has $[/tex]9 more than Deon:
[tex]\[ x + 9 = 15 + 9 = 24 \][/tex]
- Christine has [tex]$24. 7. Calculate Alan's Amount: - Alan has 4 times what Deon has: \[ 4x = 4 \times 15 = 60 \] - Alan has $[/tex]60.
8. Conclusion:
- Deon has [tex]$15, Christine has $[/tex]24, and Alan has [tex]$60. Therefore, Deon has $[/tex]15, Christine has [tex]$24, and Alan has $[/tex]60.
1. Define Variables:
- Let [tex]\( x \)[/tex] represent the amount of money Deon has.
2. Express Christine's and Alan's Amounts in Terms of [tex]\( x \)[/tex]:
- Christine has [tex]$9 more than Deon. Thus, Christine has \( x + 9 \) dollars. - Alan has 4 times what Deon has. Hence, Alan has \( 4x \) dollars. 3. Set Up the Equation: - The total amount of money they have is $[/tex]99.
- Therefore, we can set up the following equation:
[tex]\[ x (Deon) + (x + 9) (Christine) + (4x) (Alan) = 99 \][/tex]
4. Combine Like Terms:
[tex]\[ x + x + 9 + 4x = 99 \][/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 6x + 9 = 99 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Subtract 9 from both sides:
[tex]\[ 6x = 90 \][/tex]
- Divide by 6:
[tex]\[ x = 15 \][/tex]
- Thus, Deon has [tex]$15. 6. Calculate Christine's Amount: - Christine has $[/tex]9 more than Deon:
[tex]\[ x + 9 = 15 + 9 = 24 \][/tex]
- Christine has [tex]$24. 7. Calculate Alan's Amount: - Alan has 4 times what Deon has: \[ 4x = 4 \times 15 = 60 \] - Alan has $[/tex]60.
8. Conclusion:
- Deon has [tex]$15, Christine has $[/tex]24, and Alan has [tex]$60. Therefore, Deon has $[/tex]15, Christine has [tex]$24, and Alan has $[/tex]60.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.