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Find two numbers if their sum is 80 and their difference is 12

2 Answers

2 votes

Answer:

The numbers are 34 and 46.

Explanation:

Let x be the first number

y be the second number

x + y = 80 ----1st equation

x - y = 12 -----2nd equation

from equation 2

x - y = 12

x = 12 + y ---equation 2'

Substitute equation 2' to equation 1

x + y = 80

(12 + y) + y = 80

2y = 80 - 12

2y = 68

y = 34

Substitute y = 34 to equation 2'

x = 12 + y

x = 12 + 34

x = 46

User Ben Rondeau
by
8.0k points
3 votes

Answer:

The numbers are 34 and 46

Explanation:

Using the information provided, we are going to set up a system of equations, solve for one number, plug it back into one of the equations, and solve for the second number.

First, it gives us the sum of two numbers is 80. So let a = the first number and b = the second number. Sum tells us the two of these numbers added together is 80. So the first equation is:
a + b = 80

Next, it gives us the difference between the two numbers is 12. So:
a - b = 12.

Our system of equations is
a + b = 80
a - b = 12

With this, we combine like terms and solve for the variable that is left.
a + b + a - b = 80 + 12
a + a + b - b = 92
2a 0 = 92
2a = 92
Divide both sides by 2
2a / 2 = 92 / 2
a = 46

Now we plug 46 as a into one of the equations. I suggest the top equation, a + b = 80. So:
46 + b = 80
Subtract 46 from both sides
46 - 46 + b = 80 - 46
b + 0 = 34
b = 34

To check, let's plug both a and b into the second equation, a - b = 12
46 - 34 = 12
12 = 12 ✅

User Michalhosna
by
8.2k points

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