Solve For Unknowns & Verify: Math Problems Explained

Hey guys! Let's dive into some cool math problems where we need to find the missing numbers and then double-check our answers to make sure they're spot on. It's like being a math detective! We'll break down each problem step by step, so it's super easy to follow. Get ready to sharpen those pencils and put on your thinking caps!

43,547 + a = 245,602

Okay, let's kick things off with our first equation: 43,547 + a = 245,602. In this equation, we're trying to figure out what the value of 'a' is. 'A' is our mystery number, the unknown we're hunting for. The equation tells us that if we add 43,547 to 'a', we should end up with 245,602. So, how do we find 'a'? The key here is to use the inverse operation. Since we're adding 43,547 to 'a', we need to do the opposite – we need to subtract 43,547 from both sides of the equation. This is a fundamental principle in algebra: whatever you do to one side of the equation, you must do to the other to keep things balanced. Think of it like a seesaw; if you add weight to one side, you need to add the same weight to the other side to keep it level.

So, let's subtract 43,547 from both sides:

245,602 - 43,547 = a

Now, it's just a matter of doing the subtraction. You can do this by hand, lining up the numbers and borrowing as needed, or you can use a calculator. Either way, you should find that 245,602 minus 43,547 equals 202,055. So, we've found our 'a'!

a = 202,055

But we're not done yet! Remember, we need to verify our solution. This is like checking our detective work to make sure we've got the right culprit. To verify, we simply plug our value for 'a' back into the original equation:

43,547 + 202,055 = 245,602

Now, we add 43,547 and 202,055. If our calculation is correct, the result should be 245,602. Go ahead and try it! You'll find that indeed, 43,547 + 202,055 does equal 245,602. That means our solution for 'a' is correct! We've successfully solved the equation and verified our answer. Great job!

a = b - 45,555

Next up, we have the equation a = b - 45,555. This one looks a little different because we have two unknowns, 'a' and 'b'. This means we can't find a single numerical value for either 'a' or 'b' without more information. Instead, we can express 'a' in terms of 'b', or 'b' in terms of 'a'. The equation already tells us that 'a' is equal to 'b' minus 45,555. So, if we knew the value of 'b', we could easily find 'a'. But since we don't, we'll leave it like this for now. Sometimes in math, you don't get a single number as an answer, and that's okay! You might get an expression or a relationship between variables.

Let's say we wanted to find 'b' in terms of 'a'. To do that, we would need to isolate 'b' on one side of the equation. Right now, we're subtracting 45,555 from 'b'. To undo that subtraction, we need to add 45,555 to both sides of the equation. Remember, we have to keep the equation balanced!

So, let's add 45,555 to both sides:

a + 45,555 = b - 45,555 + 45,555

The -45,555 and +45,555 on the right side cancel each other out, leaving us with:

a + 45,555 = b

Now we have 'b' expressed in terms of 'a'. This tells us that 'b' is equal to 'a' plus 45,555. Again, without knowing the value of 'a', we can't find a specific number for 'b'. But we've successfully rearranged the equation to express 'b' in terms of 'a'.

Since we can't get a single numerical answer for 'a' or 'b' in this case, there's nothing specific to verify numerically. However, we can verify that our rearrangement of the equation is correct. We started with a = b - 45,555 and rearranged it to b = a + 45,555. If we were to subtract 45,555 from both sides of b = a + 45,555, we should get back our original equation. Try it! You'll see that it works. This gives us confidence that our algebraic manipulation was correct.

125,435 a =

Alright, let's tackle the next one: 125,435 a =. It seems like there might be a missing part of the equation here. Equations usually have an equals sign (=) and something on both sides. In this case, we have 125,435 multiplied by 'a' on the left side, but we don't know what it's supposed to equal on the right side. Without the other side of the equation, we can't solve for 'a'. It's like having only half of a puzzle – we can see some of the pieces, but we can't complete the picture.

If there were a number on the right side, we could solve for 'a' by dividing both sides of the equation by 125,435. For example, if the equation were 125,435 a = 250,870, we would divide both sides by 125,435 to get a = 2. But without that other number, we're stuck. It's super important to have all the parts of the equation to be able to solve it.

So, for this problem, since we're missing information, we can't find a specific value for 'a'. We need the complete equation to move forward. It's a good reminder that in math, paying attention to all the details is key! Make sure you have all the information you need before you start trying to solve a problem. It's like following a recipe – you need all the ingredients to bake a cake!

750,000 - c = 345,500

Last but not least, let's dive into this equation: 750,000 - c = 345,500. In this problem, we need to figure out what 'c' is. 'C' is the number that, when subtracted from 750,000, gives us 345,500. So, how do we find 'c'? Just like in our first problem, we'll use the inverse operation. Here, we're subtracting 'c', so to isolate 'c', we need to do the opposite – we need to add 'c' to both sides of the equation. But there's a slightly easier way to think about it in this case.

We can also think of this as: we want to get 'c' by itself on one side. To do that, we need to move the 345,500 to the other side. Since 345,500 is being added (even though there's a minus sign in front of the 'c', the 345,500 is positive), we need to subtract 345,500 from both sides:

750,000 - c - 345,500 = 345,500 - 345,500

This simplifies to:

750,000 - 345,500 - c = 0

Now, let's subtract 345,500 from 750,000:

404,500 - c = 0

Now, to get 'c' by itself, we can add 'c' to both sides:

404,500 = c

So, we've found that c = 404,500!

But we're not done yet – we need to verify! Let's plug our value for 'c' back into the original equation:

750,000 - 404,500 = 345,500

Now, subtract 404,500 from 750,000. If our calculation is correct, the result should be 345,500. And guess what? It is! 750,000 - 404,500 does indeed equal 345,500. That means our solution for 'c' is correct. High five!

Wrapping Up

So, guys, we've tackled some awesome math problems today! We solved for unknowns, rearranged equations, and verified our answers. Remember, the key to solving equations is to use inverse operations and keep the equation balanced. And always, always verify your solutions to make sure you're on the right track. Keep practicing, and you'll become math superstars in no time!