Question

The sum of three integers is 12

Answer 1

Answer:

First = 5, second = 17, third = -10

Step-by-step explanation:

First integer = x

The third integer is 15 less than the first, so

Third integer = x - 15

The second integer = y

The sum of the first and second integers exceeds the third by 32, so

The sum of the first and second integers = x + y

The third integer = x - 15

x + y is 32 more than x - 15, hence

x + y - 32 = x - 15

y - 32 = -15

y = 32 - 15

y = 17

The second integer = 17

The sum of three integers is 12, so

x + 17 + x - 15 = 12

2x + 2 = 12

2x = 12 - 2

2x = 10

x = 5

x - 15 = 5 - 15 = -10

Answer 2

The three integers are 5,17 and -10

Step-by-step explanation:

Let x, y and z be three integers then

$x+y+z=12 \ \ \Eqn\ 1$

'The sum of the first and second integers exceeds the third by 32'

$x+y=z+32\ \ \ \ Eqn\ 2$

The third integer is 15  less than the first.

$z=x-15\ \ \ \ Eqn\ 3$

From Eqn 2:

$x+y=z + 32\\x+y-z=32$

Subtracting Eqn 1 from eqn 2

$x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20$

Dividing both sides by -2

$\frac{-2z}{-2}=\frac{20}{-2}\\z=-10$

Putting z=-10 in Eqn 3

$z=x-15\\-10=x-15\\x=15-10\\x=5$

Putting x=5 and z=-10 in Eqn 1

$x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17$

Hence,

The three integers are 5,17 and -10

Keywords: Linear Equations, Variables

Learn more about linear equations at:

• brainly.com/question/13219835
• brainly.com/question/1836777

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