Understanding the Problem
To find the numbers that are in a ratio of 3:1 and sum up to 28, we first need to define the two numbers. Let's call the first number 3x and the second number x, where x is a common multiplier.
Setting Up the Equation
- The equation for the sum of the numbers is:
- 3x + x = 28
- This simplifies to:
- 4x = 28
Calculating the Values
- Now, solve for x:
- x = 28 / 4
- x = 7
- Therefore, the two numbers are:
- First number: 3x = 3 * 7 = 21
- Second number: x = 7
Finding the New Ratio
To achieve a 1:3 ratio, the first number (21) must be equal to three times the second number.
- Let the new second number be y.
- For a 1:3 ratio:
- 21 = 3y
- Solving for y gives:
- y = 21 / 3
- y = 7
Determining the Increase Needed
To find out how much the second number needs to be increased:
- Current second number = 7
- New second number required = 21 / 3 = 21/3 = 7
- The increase required:
- Increase = New second number - Current second number
- Increase = y - 7
Since we need to make the second value larger to achieve a ratio of 1:3, we realize that the second number must actually be increased to reach the new condition.
Conclusion
To summarize, the second number (currently 7) must be increased to allow for a new ratio of 1:3.
- The final increase needed:
- Increase = 21 - 7 = 14
Thus, the second number must be increased by 14 to achieve the desired ratio of 1:3.