Question

if a,b,c,d be integers where a + b + c =53 ,b+ c + d = 51, c + d + a= 57 and d + a + b is equal to 58 the greatest and smallest number among a b c d are respectively

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Answer 1

Answer:

Pls check the attachment for the answer and explanation

Answer 2

Largest number is a, a=21

Smallest number is c, c= 15.

Given:

• $a + b + c = 53...eq1$
• $b + c + d = 51...eq2$
• $c + d + a = 57...eq3$
• $d + a + b = 58...eq4$

To find:

• Find the greatest and smallest number among a,b,c, and d.

Solution:

Step 1:

Add all four equations.

$3a + 3b + 3c + 3d =53 + 51 + 57 + 58$

or

$3(a + b + c + d) = 219$

or

$\bf a + b + c + d = 73...eq5$

Step 2:

Subtract eq2 from eq5.

$a + b + c + d - b - c - d = 73 - 51$

or

$\bf \red{a = 21}$

Step 3:

Subtract eq3 from eq5.

$b = 73 - 57$

or

$\bf \red{b = 16}$

Step 4:

Subtract eq4 from eq5.

$c = 73 - 58$

or

$\bf \green{c = 15}$

Step 5:

Subtract eq1 from eq5.

$d = 73 - 53$

or

$\bf \green{d = 20}$

Thus,

Largest number is a, a=21

Smallest number is c, c= 15.

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