Unknown Number Problems: Solve With Equations

Hey guys! Math can sometimes feel like a puzzle, but don't worry, we're going to break it down together. In this article, we'll tackle some problems where we need to find an unknown number. We'll transform these problems into equations, which are just mathematical sentences with an equals sign. Think of it like this: we're going to translate word problems into math language! We will use variables to represent these unknowns and then solve for them. Sounds fun, right? So, grab your pencils and let's dive in!

a) What number added to 12 equals 80?

Let's start with the first problem. We need to find a number that, when added to 12, gives us 80. To solve this using an equation, we'll use a variable. A variable is just a symbol, usually a letter, that represents the unknown number. Let's use the letter 'x' for our unknown number. Now we can translate the problem into an equation. "What number added to 12 equals 80" becomes: x + 12 = 80. See how we turned the words into a math sentence? The next step is to isolate 'x' on one side of the equation. This means we want to get 'x' all by itself. To do this, we need to get rid of the '+ 12'. The opposite of adding 12 is subtracting 12, so we'll subtract 12 from both sides of the equation. Remember, whatever we do to one side of the equation, we must do to the other side to keep it balanced. So, our equation becomes: x + 12 - 12 = 80 - 12. Now, simplify: x = 68. That's it! We've found our unknown number. The number that, when added to 12, equals 80 is 68. To double-check, we can plug 68 back into our original equation: 68 + 12 = 80. And it works! Solving equations like this is super useful in all sorts of situations, from figuring out how much change you should get at the store to calculating measurements for a project. Keep practicing, and you'll become an equation-solving pro in no time! The key is to carefully translate the word problem into a mathematical expression, identify the unknown variable, and then use inverse operations to isolate the variable and find its value. Don't be afraid to break the problem down into smaller steps, and always double-check your answer to make sure it makes sense in the context of the original problem.

b) Find the number that, when increased by 48, equals 71.

Okay, let's move on to the second problem. This time, we're looking for a number that, when increased by 48, gives us 71. Again, we'll use a variable to represent our unknown number. Let's stick with 'x' for consistency. So, "Find the number that, when increased by 48, equals 71" translates to: x + 48 = 71. Notice how "increased by" means we're adding. Just like before, our goal is to isolate 'x'. We need to get rid of the '+ 48' on the left side of the equation. To do that, we'll subtract 48 from both sides: x + 48 - 48 = 71 - 48. Simplify: x = 23. Excellent! We've found our unknown number. The number that, when increased by 48, equals 71 is 23. Let's check our answer: 23 + 48 = 71. Perfect! It checks out. You're getting the hang of this! Remember, the most important part is understanding how to translate the words into a mathematical equation. Think about what the words mean – "increased by" means addition, "decreased by" means subtraction, and so on. Once you have the equation, the rest is just algebra! Keep in mind that solving these types of problems is a foundational skill in mathematics. It's used in everything from basic arithmetic to advanced calculus. So, mastering these concepts now will set you up for success in future math courses. Don't hesitate to try different methods and strategies until you find what works best for you. Practice makes perfect, and the more problems you solve, the more confident you'll become.

c) From what number do you subtract 44 to get 35?

Alright, let's tackle the third problem. This one asks, "From what number do you subtract 44 to get 35?" We're still on the hunt for an unknown number, so let's keep using 'x'. This time, the words "subtract 44 from x" tell us we're dealing with subtraction. So, our equation is: x - 44 = 35. To isolate 'x', we need to get rid of the '- 44'. The opposite of subtracting 44 is adding 44, so we'll add 44 to both sides of the equation: x - 44 + 44 = 35 + 44. Simplify: x = 79. Great job! We found it. The number from which you subtract 44 to get 35 is 79. Let's verify: 79 - 44 = 35. It works! See how each problem is a little different, but the process of setting up the equation and solving for the unknown stays the same? That's the power of algebra! You're learning a skill that you can apply to a wide range of problems. In addition to the algebraic method, it can sometimes be helpful to visualize the problem. For instance, in this case, you could think of a number line. You start at an unknown point, move 44 units to the left (subtract 44), and end up at 35. The question then becomes, where did you start? This visual approach can help some people grasp the concept more intuitively. Remember, there's no single "right" way to approach a math problem. Find the methods that make sense to you and use them to your advantage.

d) Find the number that, when decreased by 55, equals a certain result.

Now, let's move on to the final problem. This one says, "Find the number that, when decreased by 55, equals a certain result." We're still looking for a number, so we will call our number 'x'. Here, we are using the key phrase "decreased by 55". But hold on a second! The problem doesn't tell us what the “certain result” is! Let's assume for a second that the certain result is, for example, 20. We can write this as: x - 55 = 20. Now we will solve it like previous times. To isolate the 'x', we must remove the '-55', therefore we will add 55 to both sides of the equation: x - 55 + 55 = 20 + 55. Simplify the equation: x = 75. So the number that, when decreased by 55, equals 20 is 75. It's so important to read the problem carefully and make sure you understand what it's asking. If there's information missing, you might need to make an assumption or ask for clarification. Math is all about precision, so every detail matters. Keep practicing these types of problems, and you'll become a master at translating words into equations and solving for unknowns. You are already developing essential skills for success in mathematics and beyond. Remember that the ability to think critically and solve problems is valuable in many aspects of life, so the effort you put in now will pay off in the long run.

I hope this step-by-step guide helped you understand how to solve these types of problems. Remember, practice makes perfect! The more you practice, the easier it will become. Keep up the great work, and you'll be solving equations like a pro in no time!