Question

This is due like right now, please help me!!!!

Answer 1

`\bold{\huge{\orange{\underline{ Solution }}}}`

`\bold{\underline{ Given \: Rules}}`

• The sum of the number in each of the four rows is the same
• The sum of the numbers in each of the three columns is the same
• The sum of any row does not equal the sum of any column

`\bold{\underline{ Let's \: Begin}}`

According to the Second rule :-

`\sf{ 75+b+83=76+80+d=a+81+85+78+c+e }`

`\sf{ 158 + b = 156 + d = 166 + a = 78 + c + e ...(1)}`

According to the first rule :-

`\sf{ 75+76+a+78 = b+80+81+c = 83+86+d+e}`

`\sf{ 229 + a = 161 + b + c = 168 + d + e ...(2)}`

From ( 1 ) we got :-

`\sf{ 158 + b = 166 + a, 156 + d = 166 + a }`

`\sf{ b = 166 - 158 + a, d = 166 - 156 + a }`

`\sf{ b = 8 + a, d = 10 + a ...(3)}`

Subsitute (3) in ( 2 ) :-

`\sf{229+a = 161+8+a+c = 168+10+a+e}`

`\sf{ 229+a = 169+a+c = 178+a+e}`

We can write it as :-

`\sf{ 229+a = 169+a+c \:or\:229+a = 178+a+e}`

`\sf{ c = 299-169+a-a\:or\:e = 229-178+a-a}`

`\sf{ c = 60 \: and \: e = 51 }`

Subsitute the value of c and e in ( 1 ):-

`\sf{ 158 + b = 156 + d = 166 + a = 78 + 60 + 51 }`

`\sf{ 158 + b = 156 + d = 166 + a = 189}`

Now,

`\sf{ For \: b, 158 + b = 189 }`

`\sf{ b = 189 - 158 }`

`\sf{ b = 31}`

`\sf{ For \: d , 156 + b = 189 }`

`\sf{ d = 189 - 156 }`

`\sf{ d = 33}`

`\sf{ For \: a, 166 + a = 189 }`

`\sf{ a = 189 - 166 }`

`\sf{ a = 23 }`

Hence, The value of a, b, c, d and e is 23, 31 ,60 ,33 and 51 .