the sum of 2 numbers is 53. Their difference is 33. What are the numbers? Please explain how to work this.?

Answer 1

This is known as solving a system. It is often taught in Algebra, and will eventually lead into Matrix (or Linear) Algebra.

The idea is that you have two unknowns. If you had only one unknown would need at least one equation to solve it. Like in basic algebra... 3x+6=9

Since you have two unknowns, you will need at least two equations. Which you have.

The sum of two numbers... x+y ... is equal to 53
The difference of two numbers... x-y ... is equal to 33
Your system is:

x + y = 53
x - y = 33
...and you will solve this simultaneously.

There are a few different ways to do this. For this problem the easiest way would be elimination. With this method you basically add the "x"s together, the "y"s together, and the integers together; as if the two equations were connected with an addition sign.

x + y = 53
x - y = 33
--------------
2x + 0y = 86

Solve for x ... then plug and chug, or replace "x" with it's solution.

2x = 86 ... x=43

x + y = 53 ... (43) + y = 53 ... y = 10

x=43 ... y = 10 ...

Always check your solution:

x+y=53 ... (43) + (10) = 53 ... 53=53
x-y=33 ... (43) - (10) = 33 ... 33=33

...Hope this helps

Answer 2

By inspection, one of the numbers is 10. More generally, we can write x + y = 53; x - y = 33; and the solution is straightforward: the simplest way is to just add the equations, getting 2x = 86. So, x = 43 and y is easily found.

Answer 3

a million) nicely in the beginning we can discover that the unique quantity is 40 9, by way of fact it reported that the end result replaced into 40. next, the ratio 3:4. we can upload them at the same time to make 7, and then divide 40 9 by using 7 to make certain how a lot the three and the 4 could be more advantageous by using. 40 9/7 = 7 So cases 3 by using 7, and four by using 7, to discover the ensuing ratio, that's: 21:28 The better form of the two is 28. answer a million: 28 2) comparable thought. upload at the same time to get 11, divide one hundred sixty five by using 11 to get 15. Multiply the three diverse numbers by using 15 to get the final ratio, ensuing in: 30:40 5:ninety Getting the entire ratio enables us to additionally verify it fairly is right. upload them at the same time and it consists of one hundred sixty five, so all of us know it fairly is best suited. the adaptation between the better and least quantity is 60. answer 2: 60 wish this enables :)

Answer 4

the sum of 2 numbers is 53

x + y = 53

Their difference is 33

x - y = 33

Add the equations together

x + y = 53
x - y = 33

2x = 86
x = 43

Substitute the value for x into the first equation

43 + y = 53
y = 10
.

Answer 5

x + y = 53 . .. equation 1
x - y = 33 . . . equation 2 . . . adding
2x = 86
x = 43
y = x - 33 = 10

Answer 6

x + y = 53
y = 53 - x

x - y = 33
x - (53 - x) = 33
2x - 53 = 33
2x = 86
x = 43
y = 10

The numbers are 10 and 43