Answer :
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.
