The sum of two positive numbers is 37, and their difference is 7. If [tex]$x$[/tex] and [tex]$y$[/tex] represent the unknown numbers, which two equations belong to the system of equations that represents this situation?
[tex]$x=y+37$[/tex]
[tex]$x-y=37$[/tex]
[tex]$x+y=37$[/tex]
[tex]$x-y=7$[/tex]
[tex]$x+y=7$[/tex]
Answer (2)
The two equations that represent the situation are x + y = 37 and x − y = 7 . These equations reflect the sum and difference of the two numbers described in the problem. Therefore, the correct answer is: x + y = 37 and x − y = 7 .
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The problem states that the sum of two numbers is 37, which translates to the equation x + y = 37 .
The problem also states that the difference of the same two numbers is 7, which translates to the equation x − y = 7 .
Therefore, the two equations that represent the situation are x + y = 37 and x − y = 7 .
The equations that represent this situation are x + y = 37 and x − y = 7 .
Explanation
Problem Analysis Let's analyze the problem. We are given two pieces of information about two unknown numbers, x and y . The first piece of information is that their sum is 37, and the second piece of information is that their difference is 7. We need to translate these two pieces of information into two equations.
Translating the First Statement The first statement, "The sum of two positive numbers is 37", can be directly translated into the equation: x + y = 37
Translating the Second Statement The second statement, "their difference is 7", can be directly translated into the equation: x − y = 7
Identifying the Equations Therefore, the two equations that represent the given situation are x + y = 37 and x − y = 7 .
Examples
Imagine you and a friend are collecting seashells on the beach. Together, you collected 37 seashells. You know that you collected 7 more seashells than your friend. This problem is analogous to finding out how many seashells each of you collected individually. By setting up a system of equations, you can determine the number of seashells each person found, just like we found the two unknown numbers in the original problem. This kind of problem helps in resource allocation, determining quantities, and understanding relationships between different variables in real-life scenarios.
