Math Problem Statement
Solution
The problem from the image states:
b. There are two numbers. The first number minus the second number is 15. One-third of the sum of the numbers is one-quarter of the first number. What are the two numbers?
Let's define:
- The first number as
- The second number as
We are given two conditions:
- The first number minus the second number is 15:
- One-third of the sum of the numbers is one-quarter of the first number:
Solving the system:
From Equation 1, we can solve for :
Substitute this into Equation 2: Simplify the left side: Multiply both sides by 12 to eliminate the denominators: Expand and solve:
Now, substitute back into Equation 1:
Thus, the two numbers are 12 and -3.
Would you like more details or have any questions?
Related Questions:
- How would the solution change if the sum condition were different?
- Can you graphically represent the two equations to find the intersection?
- What would happen if the difference between the numbers was another value, like 20?
- Can you create another riddle using similar relationships between two numbers?
- How would you set up the problem if the sum of the numbers was twice the first number?
Tip: Always check your solutions by substituting the values back into the original equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
x - y = 15
(1/3)(x + y) = (1/4)x
Theorems
Equation manipulation and substitution method
Suitable Grade Level
Grades 7-9
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