Solve 3q+r When Q=3 And R=7

Hey guys! Let's dive into a super straightforward math problem today. We're asked to find the value of the expression $3q+r$ given that $q=3$ and $r=7$. This is a basic algebra concept where we substitute given values into an expression to find its numerical result. It's like solving a little puzzle where you're given the pieces and just need to put them together. We'll break it down step-by-step, so even if math isn't your favorite subject, you can follow along and see how easy it can be. Get ready to flex those brain muscles, and let's get this problem solved!

Understanding the Expression: $3q+r$

Alright, let's get cozy with this expression: $3q+r$. What does it mean? When we see a number right next to a letter like 'q' in algebra, it means multiplication. So, $3q$ actually means 3 multiplied by q. The '+' sign is our good old addition, so we'll be adding the result of $3q$ to the value of $r$. The problem gives us the exact values for $q$ and $r$. We have $q = 3$ and $r = 7$. Our mission, should we choose to accept it, is to replace every 'q' with '3' and every 'r' with '7' in the expression $3q+r$. This process is called substitution, and it's a fundamental skill in algebra. Think of it like swapping out ingredients in a recipe – you're replacing the variables with their specific numerical values to see what the final dish (or in this case, the final number) will be. It's crucial to be careful during substitution to ensure you're placing the numbers in the correct spots and not mixing them up. This carefulness will lead us to the correct answer among the options provided. So, let's meticulously perform this substitution to unlock the value of $3q+r$.

Substituting the Values: $q=3$ and $r=7$

Now for the fun part, the actual substitution! We have our expression: $3q+r$. And we know that $q=3$ and $r=7$. So, we're going to take the number '3' and put it wherever we see 'q', and we're going to take the number '7' and put it wherever we see 'r'. This is where we need to be super precise, guys. Let's rewrite the expression by replacing the variables.

First, let's focus on the term $3q$. Since $q=3$, we replace 'q' with '3'. So, $3q$ becomes $3 imes 3$. Remember, the '3' in front of 'q' means we multiply. So, $3 imes 3$ equals 9.

Next, we look at the term $+r$. Since $r=7$, we replace 'r' with '7'. So, $+r$ becomes $+7$.

Now, we put it all together. Our original expression $3q+r$ has now transformed into $9 + 7$ after our substitutions. See? It’s not so scary after all! We've successfully turned an algebraic expression into a simple arithmetic problem. The next step is to calculate this sum, which is the final calculation needed to solve the problem. This substitution step is critical; any error here will lead to the wrong final answer. So, double-checking your substitutions is always a smart move in these kinds of math challenges.

Calculating the Result: $9+7$

We've done the heavy lifting with the substitution, and now we're left with a simple addition problem: $9 + 7$. This is where we just need to perform the calculation to find our final answer. Adding 9 and 7 is pretty straightforward. If you think of it on a number line, starting at 9 and moving 7 steps forward, you'll land on 16. Alternatively, you can break it down: 9 + 1 is 10, and then you have 6 more to add (since 7 = 1 + 6), so 10 + 6 equals 16. Or, you can simply recall your addition facts. The sum of 9 and 7 is 16.

So, when $q=3$ and $r=7$, the value of the expression $3q+r$ is 16. This is our final numerical answer. We've successfully navigated the problem from an algebraic expression to a concrete number. It's a great feeling to solve these kinds of problems, right? We've used substitution and basic arithmetic to arrive at our solution. Now, let's compare this result with the given options to find the correct answer choice.

Comparing with the Options

We have arrived at our answer, which is 16. Now, let's look at the options provided in the question to see which one matches our calculated value. The options are:

A. 24 B. 63 C. 16 D. 13

Our calculated result is 16. Let's check if this matches any of the options.

• Option A is 24. This does not match our answer.
• Option B is 63. This also does not match our answer.
• Option C is 16. Bingo! This perfectly matches our calculated value.
• Option D is 13. This does not match our answer.

Therefore, the correct option is C. 16. We found the value of $3q+r$ by substituting $q=3$ and $r=7$ into the expression, which gave us $3(3) + 7 = 9 + 7 = 16$. It's always satisfying when your answer aligns with one of the choices, confirming your work. This problem really highlights the importance of careful substitution and accurate calculation in mathematics. Keep practicing these fundamental skills, and you'll be solving even more complex problems in no time!

Why This Matters in Mathematics

So, why do we bother with problems like this? You might be thinking, "Okay, I can plug in numbers, but what's the big deal?" Well, guys, this simple act of substitution and evaluation is the bedrock of so much of mathematics, especially algebra. Think about it: every formula you encounter, from calculating the area of a circle ($A = \pi r^2$) to figuring out projectile motion in physics, requires you to substitute values into an equation or expression. When scientists or engineers design a bridge, a new piece of software, or even a medical treatment, they are constantly plugging numbers into complex mathematical models to predict outcomes and ensure safety. This problem, $3q+r$, is a miniature version of that process. It teaches us how to handle variables, how to perform operations in the correct order (though this one was straightforward with just multiplication and addition), and how to arrive at a definitive answer. Mastering these basic skills means you're building a strong foundation for tackling more challenging mathematical concepts later on. It's about developing logical thinking and problem-solving abilities that extend far beyond the classroom. So, the next time you solve a problem like this, remember you're practicing skills that are essential for innovation and understanding the world around us. It’s all about building that mathematical toolkit, piece by piece!