Solution
- The larger number is x and the smaller number is y
Sentence 1:
- "The sum of two numbers is 64"
- This means that when we add x and y, we get 64. Mathematically, this is represented as:
[tex]x+y=64\text{ (Equation 1)}[/tex]Sentence 2:
- "The difference of the two numbers is 18"
- Since x is the larger number, it means that when we subtract y from x we get 18. Mathematically, we have:
[tex]x-y=18\text{ (Equation 2)}[/tex]- Now that we have two equations relating x and y, we can solve them simultaneously and find the values of x and y.
- We shall apply the elimination method to solve. We would be subtracting both equations to find the value of y and after we get the value of y, we can then substitute this value of y into any of the equations, 1 or 2 to find the value of x.
- Let us perform these operations below:
[tex]\begin{gathered} x+y=64\text{ (Equation 1)} \\ x-y=18\text{ (Equation 2)} \\ \\ \text{ Subtract both equations} \\ \\ x+y-(x-y)=64-18 \\ x+y-x+y=46 \\ 2y=46 \\ \text{Divide both sides by 2} \\ y=\frac{46}{2} \\ \\ y=23 \\ \\ \text{Substituting the value of }y\text{ into equation 2} \\ x-y=18 \\ x-23=18 \\ \text{Add 23 to both sides} \\ x=23+18 \\ \therefore x=41 \end{gathered}[/tex]Final Answer
The answers to the question are:
[tex]\begin{gathered} x=41 \\ y=23 \end{gathered}[/tex]
