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SIZIF [17.4K]
3 years ago
15

The sum of three integers is 189. The first integer is 28 less than the second. The second integer is 21 less than the sum of th

e first and third integer. Find the three integers
Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0

Answer:

The first integer is 56

The second integer is 84

The third integer is 49

Step-by-step explanation:

Define the variables

Let

x ----> the first integer

y ----> the second integer

z ----> the third integer

we know that

x+y+z=189 ----> equation A

x=y-28 ----> y=x+28 ----> equation B

y=(x+z)-21 ----> equation C

Equate equations B and C

(x+z)-21=x+28

subtract x both sides

z-21=28

Adds 21 both sides

z=28+21

z=49

substitute the value of z in equation A

x+y+49=189

x+y=189-49

x+y=140 -----> equation D

Solve the system of equations B and D

y=x+28 ----> equation B

x+y=140 -----> equation D

substitute equation B in equation D and solve for x

x+x+28=140

2x+28=140

2x=140-28

2x=112

x=56

<em>Find the value of y</em>

y=x+28 -----> y=56+28=84

therefore

The first integer is 56

The second integer is 84

The third integer is 49

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