if a-b=28 and a+b=46.Then find the value of b?
Answers
Answer:
Interesting. A basic algebra problem has 273 collapsed answers and as a question topic. I suspect that the OP isn't interested in the conventional solution to the problem. I'm not even sure whether the question is mathematical in nature. Even so, I present a solution that, while in essence mathematical, is different enough to justify its existence.
Before I begin the solution, here are my assumptions:-
a refers to a quantity of something
b also refers to a quantity of something that may or may not be equal to a.
'+' refers to addition. a+b means that b is added to a. The implication is that a and b refer to quantities of the same kind of thing. Addition of different kinds of things is meaningless. 2 apples added to 3 apples gives 5 apples. Addition of 3 apples and 4 oranges changes nothing. The result is still 3 apples and 4 oranges. The idea that only 'like' things can be added is called dimensional homogeneity [1]. This principle is used by physicists and engineers to discover fundamental relations between physical quantities and to check the validity of equations.
'-' refers to subtraction. a−b means that b is removed from a. Again, the equation must be homogeneous. 'I removed 3 horses from a group of donkeys' is nonsense. Only 'like' quantities can be subjected to this operation.
'=' refers to equals. The result of all operations on the left of '=' is written to its right.
With that out of the way, let's get down to business. Imagine a glass of water that is half filled (or empty. Your choice). Like this one.
a refers to a quantity. Any quantity. Like weight, length, luminosity, anything really. Say the water in the glass weighs a units. Here's the same glass placed on a weighing scale.
Please excuse my deplorable drawing skills. Here are two such half filled glasses.
Now, pour some water from the right glass into the left one. Let's call the weight of the quantity poured b. Our setup after adding weighing scales now looks like this.
Wait. We know that a+b is equal to 6 units and a−b is equal to 2 units. That means that our setup actually looks like this:
Let's play around. I'll pour all the water from the right glass into the left one. Since both glasses were initially half filled, the left one is now filled to the brim.
We see that the full glass weighs 8 units. a is the weight of the half filled glass. Instantly, we can infer that a is equal to half of 8 units ie:- 4 units.
What we have done here is effectively
(a+b)+(a−b)=2a
2a=8
a=4
We now know what a is. To find b pour out half of the water from the left glass to the right one and we return to the initial state.
Start pouring water from the right glass into the left till the scale displays '6' units. That's when you know that the weight of water in the left glass is a+b . Pour the remaining water in the right glass into the sink (or drink it. Just make it disappear). This the current state of our setup.
Start pouring water from the left glass into the right one till the right glass is half filled. Since the weight of a half filled glass is a, the weight of the water remaining in the left one is equal to b. The setup looks like this:
That's not quite right. What you'll actually see on scales are the values of the weights, not two letters. You can see that b equals 2 just by looking at the left scale. What we have done is effectively (a+b)−a=b=2
This makes sense because the left glass weighed 6 units, we poured out 4 units and we are left with 2 units. Finally, we end up with the result
a=4
b=2
Does this result have any deeper meaning? I cannot say. However, it's worth examining whether the assumptions I made initially are valid. For instance, if I had pink paint instead of water in the two glasses and the scales measured 'pinkness' instead of weight, what will I get if pour the contents of the right one into the left one, will the paint in the left glass become twice as pink? No, it remains just as pink.
Am I making a mistake here? What does it really mean to add pinkness? The colour pink is some combination of Red, Green and Blue[2]. Amaranth Pink is [241, 156, 187] and Baby Pink is [244, 194, 194] in RGB [3]. The difference between the two is [3,38,7]. That means Baby pink has 3 units of redness, 38 units of greenness and 7 units of blueness more than Amaranth pink. We have a contradiction. Dimensional homogeneity implies that only 'like' quantities can be added but here, we have added other colours to get a different shade of pink.
One way out of this conundrum is to define pinkness as some constant ratio of Red, Green and Blue that can be added to a shade of pink to get another shade of pink. In that case, what do I get when I add 1.5*[3,38,7] to Baby pink? The sum ie:- [ 248, 251, 204] in RGB results in:
I don't know about you but this doesn't look like pink to me. Further speculation about the nature of pinkness is left as an exercise to the reader.
Answer:
9
Step-by-step explanation:
By adding both equations we get
2a = 74
a= 37
Now put the value of a in equation 2 we get
37+b= 46
b= 9
I hope answer will help you so