One number is 4 more than another, and their sum is 60 What is the smaller number? If \( x= \) the larger number and \( y \) = the smaller number, then which of the following systems could be used to solve the problem? \( \begin{array}{l}x+y=60 \text { and } x-y=4 \\ x+y=60 \text { and } x+y=4\end{array} \)

To solve for the smaller number, we can set up a system of equations based on the information given. We know that the larger number \( x \) is 4 more than the smaller number \( y \), which we can express as \( x = y + 4 \). Additionally, we know their sum is 60, so we also have \( x + y = 60 \). Therefore, the correct system of equations is \( x + y = 60 \) and \( x - y = 4 \). Now, let’s find the value of \( y \). By substituting \( x \) in the first equation using \( x = y + 4 \): \((y + 4) + y = 60\) simplifies to \(2y + 4 = 60\). Solving for \(y\), we get \(2y = 56\) or \(y = 28\). So the smaller number is 28! A little historical nugget: Systems of equations have their roots tracing back to ancient civilizations! The Babylonians were adept at solving linear equations as far back as 2000 BCE, using geometric methods — clever, right? For a practical twist, real-life situations often require you to set up equations like this when budgeting or planning. For instance, if one item costs more due to extra features, you could represent the prices as a system of equations to determine how much each item costs based on a total budget. It’s a handy tool for decision-making!