Question

puzzle question
____+_____=8
+. +.
____- _____= 6
=. =
13. 8

​

Answer 1

Given

$\boxed{}\:+\:\boxed{}\:=\:8\\+\:\:\:\:\:\:+\\ \boxed{}\:-\:\boxed{}\:=6\\=\:\:\:\:\:\:=\\13\:\:\:\:\:8$

To find

We have to find the blank spaces or numbers.

Assumption

$\boxed{a}\:+\:\boxed{b}\:=\:8\\+\:\: \: \:\:\:\:\:\:+\\ \boxed{c}\:-\:\boxed{d}\:=\:6 \\=\: \:\:\:\:\:\:\:\:\:=\\ 13\:\:\:\:\:\:\: \:\:8$

Solution

We have to find the numbers whose sum (means sum of a and b) is 8.

So we have, a + b = 8, c - d = 6, a + c = 13 and b + d = 8

As per assumption;

⇒ a + b = 8

⇒ a = 8 - b...........(eq 1)

⇒ a + c = 13

Substitute value of a above

⇒ (8 - b) + c = 13

⇒ 8 - b + c = 13

⇒ - b + c = 5

⇒ c = 5 + b..........(eq 2)

Similarly, c - d = 6

Substitute value of c above

⇒ 5 + b - d = 6

⇒ b - d = 1

⇒ b = 1 + d...........(eq 3)

We have b + d = 8.

Now, put value of b i.e. of (eq 3) above

⇒ 1 + d + d = 8

⇒ 2d = 7

⇒ d = 7/2

⇒ d = 3.5

Now, substitute value of d in (eq 3)

⇒ b = 1 + 3.5

⇒ b = 4.5

Substitute value of b = 4.5 in (eq 2)

⇒ c = 5 + 4.5

⇒ c = 9.5

Substitute value of c = 9.5 in (a + c = 13)

⇒ a + 9.5 = 13

⇒ a = 13 - 9.5

⇒ a = 3.5

Therefore,

$\boxed{3.5}\:+\:\boxed{4.5}\:=\:8\\+\: \:\:\:\:\:\:\:\:\:\:\:\:\:\:+\\ \boxed{9.5}\: -\: \boxed{3.5}\:=6 \\=\:\:\:\:\:\:\:\:\:\:\:\:\:\: \:\:= \\13\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: 8$

Answer 2

Answer:

Answers:-

⇒ a = 3.5

⇒ x = 4.5

⇒ y = 9.5

⇒ z = 3.5

Correct question:-

${\boxed{}} + {\boxed{}} = 8 \\ + \: \: \: \: \: + \\{\boxed{}} - {\boxed{}} = 6 \\ = \: \: \: \: \: = \\ 13 \: \: \: \: \: 8$

Solution:-

Let the blanks be a , x, y, z respectively.

$\rule{100}{2}$

Given equations:-

⇒ a + x = 8_________(i)

⇒ y - z = 6_________(ii)

⇒ a + y = 13________(iii)

⇒ x + z = 8_________(iv)

From (i) we get:-

⇒ a = 8 - x __________(1)

Putting value of a in (iii):-

⇒ 8 - x + y = 13

⇒ y = 13 + x - 8

⇒ y = x + 5__________(2)

Putting value of y in (ii):-

⇒ x + 5 - z = 6

⇒ x + 5 - 6 = z

⇒ z = x - 1_________(3)

Putting value of z in (iv):-

⇒ x + x - 1 = 8

⇒ 2x = 8 + 1

⇒ 2x = 9

⇒ x = 9/2

⇒ x = ${\boxed{\sf\red{4.5}}}$

$\rule{100}{1}$

Now,putting value of x in (1):-

⇒ a = 8 - 4.5

⇒ a = ${\boxed{\sf\green{3.5}}}$

$\rule{100}{2}$

Putting value of x in (2) :-

⇒ y = 4.5 + 5

⇒ y = ${\boxed{\sf\blue{9.5}}}$

$\rule{100}{2}$

Putting value of x in (3) :-

⇒ z = 4.5 - 1

⇒ z = ${\boxed{\sf\pink{3.5}}}$

So the answer:-

${\boxed{3.5}} + {\boxed{4.5}} = 8 \\ \: \: + \: \: \: \: \: \: \: \: \: \: \: + \\{\boxed{9.5}} - {\boxed{3.5}} = 6 \\ \: \: = \: \: \: \: \:\: \: \: \: \: \: = \\ \: \: 13 \: \: \: \: \:\: \: \: \: \: \: \: 8$