I am thinking of two numbers. The first number added to the second number is 5. Twice the first number added to twice the second number is 10. What are the numbers. ?????
1&4
1 and 4 works.
To determine the two numbers, let's use algebraic equations and solve for the unknown values.
Let's assume the first number is "x" and the second number is "y."
From the information given, we can create two equations:
1. x + y = 5 (The first number added to the second number is 5)
2. 2x + 2y = 10 (Twice the first number added to twice the second number is 10)
To solve these equations, we can use the method of substitution or elimination.
Using the method of substitution:
1. Rearrange the first equation to solve for x:
x = 5 - y
2. Substitute the value of x in the second equation:
2(5 - y) + 2y = 10
Simplify:
10 - 2y + 2y = 10
The y terms cancel each other out, leaving us with:
10 = 10
This equation is always true, which indicates that y can have any value.
3. With the value of y being variable, we can substitute it back into the first equation to solve for x:
x + y = 5
x + (any value) = 5
This equation suggests that x can be any number as long as it sums up to 5 with y.
Therefore, there are an infinite number of possible solutions for this problem. Some examples of potential solutions could be (1, 4), (2, 3), (3, 2), (4, 1), and so on.