Problem 201 - 1,001 GED Practice Questions For Dummies

Question

Two years ago, Sammy was 5 years younger than Michael is today. f Michael is currently \(M\) years old, how old will Sammy be 10 years from now? A) \(M-5\) B) \(M+2\) C) \(M+7\)

Step-by-Step Solution

Answer

C) \( M + 7 \)

Step 1: Define Variables

Start by recognizing what the problem gives us: Michael's current age, which is denoted as \( M \), and the relation of Sammy's age to Michael's, specifically that two years ago Sammy was 5 years younger than Michael is presently. Therefore, we can write Sammy's age two years ago as \( M - 5 \).

Step 2: Add Time to Sammy's Age

We know that two years have already passed since Sammy was \( M - 5 \) years old, which means Sammy's current age is \( M - 5 + 2 = M - 3 \).

Step 3: Predict Sammy's Future Age

The question asks us about Sammy's age 10 years from now. So we add 10 to Sammy's current age \( M - 3 \). This gives us \( M - 3 + 10 = M + 7 \). This means that Sammy will be \( M + 7 \) years old 10 years from now.

Step 4: Review and choose the Correct Answer

Looking at the options, we can see that option C is \( M + 7 \), which matches our calculated value for Sammy's age in 10 years. Hence, the correct answer is option C, \( M + 7 \).

Key Concepts

Age-related problems

Age-related problems are a common type of algebra word problem where you have to find the age of someone based on given conditions. These problems often require you to compare the ages of two or more people, as in the problem involving Sammy and Michael. Understanding the relationship between different ages helps us determine the unknown age of a person. In this particular problem, we are asked to find Sammy's age in the future based on the present age of Michael. Two years ago, Sammy was 5 years younger than Michael is now. This clue is essential because it sets the foundation of how Sammy's age is related to Michael's. By establishing that two years ago Sammy's age was diagnostically different by five years from Michael's current age, we can define variables to solve the age problem that follows.

Variable manipulation

Variable manipulation is crucial in solving algebra word problems. Variables help us represent unknown values or quantities using letters, like M for Michael's age. In the exercise with Sammy, Michael's current age is denoted by the variable \( M \). To determine Sammy's current age, we take into account where she stood in relation to Michael two years back: Sammy was \( M - 5 \) then. By adding two years to \( M - 5 \), we calculate her current age, which becomes \( M - 3 \). This step beautifully illustrates how variables help manage unknowns, transforming complex relationships into simple, solveable equations.

Equation solving

Equation solving is the heart of algebraic problems wherein we find the value of unknowns by setting up and simplifying equations. Once we have variables representing the quantities of interest, we can form equations based on the information given in the problem.For the problem at hand, after determining that Sammy's current age equates to \( M - 3 \), we need to forecast 10 years into the future. We form a simple equation, \( M - 3 + 10 \), to predict Sammy's age ten years from now, which simplifies to \( M + 7 \). By solving this equation, option C, \( M + 7 \), stands out as the correct answer. Practicing equation solving not only aids in academic success but also improves problem-solving skills in real-world scenarios. Equations enable us to bridge the logical gaps between known and unknown information effectively.