Question
Guido has a quarter of Andrés's money and three times as much as David's money. How much money does each have if the sum of all the amounts is $48,000?
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Answer to a math question Guido has a quarter of Andrés's money and three times as much as David's money. How much money does each have if the sum of all the amounts is $48,000?
Fred
4.4120 Answers
1. Declare the variable for Andrés's money: x
2. Determine Guido's money which is a quarter of Andrés's: y = \frac{x}{4}
3. Determine David's money, which is a third of Guido's: z = \frac{y}{3} = \frac{\frac{x}{4}}{3} = \frac{x}{12}
4. Write the equation that sums their total money: x + \frac{x}{4} + \frac{x}{12} = 48000
5. Get a common denominator for the fractions: x + \frac{3x}{12} + \frac{x}{12} = 48000
6. Combine the fractions: x + \frac{4x}{12} = 48000
7. Simplify the expression: x + \frac{x}{3} = 48000
8. Eliminate the fraction by multiplying by 3: 3x + x = 144000
9. Simplify further: 4x = 144000
10. Solve for x x = 36000
Final amounts:
- Andrés: x = 36000
- Guido: y = \frac{36000}{4} = 9000
- David: z = \frac{9000}{3} = 3000
2. Determine Guido's money which is a quarter of Andrés's:
3. Determine David's money, which is a third of Guido's:
4. Write the equation that sums their total money:
5. Get a common denominator for the fractions:
6. Combine the fractions:
7. Simplify the expression:
8. Eliminate the fraction by multiplying by 3:
9. Simplify further:
10. Solve for
Final amounts:
- Andrés:
- Guido:
- David:
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