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Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?
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Three fourths of one number is equal to 60% of another number and the ...
Understanding the Problem
To solve the problem, we need to define two variables based on the information provided:
- Let the first number be x.
- Let the second number be y.
Establishing Equations
From the problem, we can derive two equations:
1. Three fourths of the first number is equal to 60% of the second number:
- (3/4)x = (60/100)y
- Simplifying this gives us: 3x = 2.4y
2. The difference between these two numbers is 20:
- x - y = 20
Solving the Equations
Now, we have a system of two equations:
- 3x = 2.4y (Equation 1)
- x - y = 20 (Equation 2)
We can express y in terms of x from Equation 2:
- y = x - 20
Now, substitute y in Equation 1:
- 3x = 2.4(x - 20)
- 3x = 2.4x - 48
Now, isolate x:
- 3x - 2.4x = -48
- 0.6x = -48
- x = -48 / 0.6
- x = 80
Now, substitute x back to find y:
- y = 80 - 20
- y = 60
Final Calculation: Sum of the Numbers
Now that we have both numbers:
- x = 80
- y = 60
The sum of the two numbers is:
- Sum = x + y = 80 + 60 = 140
Conclusion
The sum of the two numbers is 140.
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Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?
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