Question

the average of 4 number is 56.the first no is 5 more than the second,the 3 no is half of the 2 and the 4 no is 3 times the sum of the first and second nos. Find the numbers​

Answer 1

Step-by-step explanation:

Let a,b,c and d be the numbers

According to given question let us form some equations,

1. a+b+c+d/4 = 56-----------> 1 eqn

2.a = b+5--------------------> 2eqn

3. c =(1/2).b------------------> 3 eqn

4. d = 3. (a+b)-------------> 4 eqn

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Now let us start solving the equations,

Substitute (2) into (4)

d = 3.(b+5+b)

d = 3.(2b+5)

d = 6b + 10

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Substitute (2), (3), and (4) into (1)

a+b+c+d/4 = 56

[b+5+b+(1/2).b+6b+15]/4 = 56

$\frac{17/2b+20}{4} =56$

Multiply both sides by 4

(17/2).b+20 = 224

Multiply both sides by 2

17b + 40 = 448

17b = 408

b = 408/17

b = 24

substitute in 2nd eqn

a=b+5

a = 24+5

a = 29

substitue in 3rd eqn

c = (1/2).b

c = (1/2).24

c = 12

substitute in 4th eqn

d = 6(24) +5

d= 144+ 15

d = 159

The numbers are 29, 24, 12, and 159

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Check:

29+24+12+159/4 = 56

224/4 = 56

56 = 56

Hence proved

Answer 2

Answer:

First number = 29

First number = 29Second number = 24

First number = 29Second number = 24Third number = 12

First number = 29Second number = 24Third number = 12Fourth number = 159

Step-by-step explanation:

Let the second number be x.

So, first number = x+5

and third number = x/2

and fourth number = 3×(x+5+x) = 3×(2x+5) = 6x+15

So,

$\frac{(x + 5) + x + \frac{x}{2}+6x + 15}{4}=56 \\ (x + 5) + x + \frac{x}{2}+6x + 15 = 224 \\ 8x + 20 + \frac{x}{2} = 224 \\ \frac{17x + 40}{2} = 224 \\ 17x + 40 = 448 \\ 17x = 408 \\ x = 24$

Therefore, First number = 29

Second number = 24

Third number = 12

Fourth number = 159

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