Question

The sum of two numbers is 100 and their difference is 80, what are the two numbers

Answer 1

The numbers are 90 and 10.

Step-by-step explanation:

Let the two numbers are x and y.

It has been given that sum of two numbers is 100. Hence, we have the equation,

x + y = 100 .........(i)

Now, the difference of these two numbers is 80. Thus, second equation is

x - y = 180......(ii)

Add equation (i) and (ii)

x + y + x - y = 100 + 80

2x = 180

Divide both sides by 2

x = 90

Substitute this value in (i)

90 + y = 100

y = 100- 90

y = 10

Therefore, the numbers are 90 and 10.

#Learn More:

The sum of two numbers is 450 and the smaller number is 120. What is the product?

Step-by-step explanation:

1. 90 and 10

Answer 2

Answer:
x=90
y=10

Step-by-step explanation:
Let x be equal to the first number.
Let y be equal to the second number.

We know that the sum of the two numbers is 100, so we can say that x+y=100.

We also know that the difference of the two numbers is 80, so we can also say that x-y=80

And now we have our two equations:

x+y=100
x-y=80

To find x and y, we first solve for one of the variables and plug it into one of the two equations to solve for the other. In this case, the easiest way to approach this question is to add both of the equations to cancel y out and solve for x (please check the picture attached for a better representation).

x+y=100
x-y=80
-> 2x=180

2x=180
Divide both sides by 2
2x/2=180/2
x=90

Now that we have found the value of the first number, x, we can plug it in to either of our two original equations to solve for y.

x+y=100
90+y=100
Subtract both sides by 90
90+y-90=100-90
y=10

Therefore, the value of x is 90 and the value of y is 10. Their sum is 100 and their difference is 80.

I hope this helps!