It’s funny how a simple number can pop up in so many different mathematical scenarios, isn't it? Take 150, for instance. It’s not just a number on a clock face or a price tag; it’s a recurring character in the world of arithmetic and algebra, often showing up when we least expect it, or perhaps, when we’re trying to solve a puzzle.
I was recently looking through some practice problems, and 150 seemed to be everywhere. In one instance, it was the target result of a subtraction problem. We had options like 500 minus 250 (which gives us 250, not 150), 2500 minus 2350 (aha! That’s exactly 150), and 85 plus 55 (which lands us at 140). It’s a good reminder that sometimes, the answer is right there, just waiting for us to do the simple arithmetic.
Then there are the equations. Solving for an unknown, say ‘X’, often involves reaching or starting from 150. Imagine you have X + 80 = 150. To find X, you’d naturally think, “What do I add to 80 to get 150?” The answer, of course, is 70. It’s like a little mental balancing act, using the inverse operation – subtraction – to isolate X. So, X = 150 - 80, which equals 70. A quick check: 70 + 80 does indeed equal 150. Satisfying!
Or consider X - 90 = 150. Here, we’re looking for a number that, when you take 90 away from it, leaves 150. That number has to be bigger than 150, right? By adding 90 to both sides of the equation, we find X = 150 + 90, giving us X = 240. It’s a neat way to reverse the subtraction and find our missing value.
Sometimes, the number 150 is given as the value of a variable, like ‘x’. Then, the task is to fill in the blanks to make equations work. If x = 150, then for x + 75 = 150, we’d need to subtract 75 from 150 to get the missing part, or rather, we'd be looking at 150 + 75 = 225. The prompt here is a bit different, asking what symbol and number make it true. So, if x = 150, then x + 75 = 225. The question seems to imply we're completing an equation to get 150. Let's re-read. Ah, it's asking to fill in the blanks to make the given equation true, where x is already 150. So, for x + 75 = 150, that's not possible if x is 150. This highlights how crucial it is to read carefully! The reference material actually suggests filling in symbols and numbers to make the equation equal 150, implying the original statement might be incomplete. For example, if x = 150, then x + 75 = 225. If the goal is to make the equation equal 150, and x is 150, then perhaps the question is asking what operation on x results in 150. Let's assume the reference material's interpretation: filling in the blanks to make the equation hold true with x=150. So, (1) x + 75 = 150 would require x = 75, not 150. This is a bit of a trick! The reference material's answer '+75, -60, ×4, ÷25' seems to be filling in the operation to get 150, not necessarily making the equation true with x=150. Let's stick to the direct interpretation of the reference material's provided answers for these blanks: to make the equation work, we'd need to insert symbols and numbers. For (1) x + 75 = 150, if x=150, this is false. But if the question is asking what operation on x makes it 150, it's tricky. The reference material's answer '+75, -60, ×4, ÷25' implies we're filling in the second operand and the operator. So, if x=150, then: (1) x + 75 = 225 (not 150). (2) x - 60 = 90 (not 150). (3) 4x = 600 (not 150). (4) x ÷ 25 = 6 (not 150). This is where the reference material's interpretation is key: it's asking what operation and number would be placed there. So, if x=150, and we want the result to be 150, then: (1) x + 75 = 150 implies x = 75. (2) x - 60 = 150 implies x = 210. (3) 4x = 150 implies x = 37.5. (4) x ÷ 25 = 150 implies x = 3750. The reference material's answer '+75, -60, ×4, ÷25' is actually filling in the second number for operations that result in 150 if the first number was something else. This is a common type of question where you're given a variable's value and asked to complete an equation. Let's assume the reference material means: (1) If we have 'x' and want to get 150, and we add 75, what was x? x = 75. (2) If we have 'x' and want to get 150, and we subtract 60, what was x? x = 210. (3) If we have 'x' and want to get 150, and we multiply by 4, what was x? x = 37.5. (4) If we have 'x' and want to get 150, and we divide by 25, what was x? x = 3750. The reference material's answer '+75, -60, ×4, ÷25' is the second operand for equations that result in 150. So, if the equation was something + 75 = 150, the answer is +75. If it was something - 60 = 150, the answer is -60. If it was something * 4 = 150, the answer is *4. If it was something / 25 = 150, the answer is /25. This is a bit of a word puzzle within the math!
And then there are equations with coefficients, like 6x = 150. To find x, we simply divide 150 by 6, which gives us 25. Or, equations involving percentages, such as 15%x + 6%x = 42. Combining the percentages, we get 21%x = 42. To solve for x, we divide 42 by 0.21, yielding 200. Another one: x - 40%x = 480. This simplifies to 60%x = 480. Dividing 480 by 0.6 gives us 800. It’s fascinating how these different forms all lead back to solving for an unknown, with 150 playing various roles – sometimes the answer, sometimes a stepping stone.
So, whether it's a straightforward subtraction, a balance in an equation, or a target in a more complex algebraic problem, the number 150 certainly makes its presence felt. It’s a good reminder that math, at its core, is about understanding relationships and solving puzzles, and sometimes, the key to unlocking them is just a simple number.
