Question

Fill the blank boxes:
\[\begin{array}{*{20}{l}}
  {\boxed{}}& + &{\boxed{}}& \Rightarrow &8 \\
   + &{}& + &{}&{} \\
  {\boxed{}}& - &{\boxed{}}& \Rightarrow &6 \\
   \Downarrow &{}& \Downarrow &{}&{} \\
  {13}&{}&8&{}&{}
\end{array}\]

Answer 1

Hint: We will solve these types of questions by filling the boxes with any variables for example, \[a\], \[b\], \[c\] and \[d\]. By forming the equations, we will find the values of missing terms.

Complete step-by-step answer:
Step 1: We will fill the blank boxes with variables as shown below:
\[\begin{array}{*{20}{l}}
  {\boxed{a}}& + &{\boxed{b}}& \Rightarrow &8 \\
   + &{}& + &{}&{} \\
  {\boxed{c}}& - &{\boxed{d}}& \Rightarrow &6 \\
   \Downarrow &{}& \Downarrow &{}&{} \\
  {13}&{}&8&{}&{}
\end{array}\]
From this, we get the following equations as below:
\[a + b = 8\], \[a + c = 13\], \[b + d = 8\]and \[c - d = 6\].
Step 2: Now, it is very clear that in the two equations \[a + b = 8\] and \[b + d = 8\] the RHS side is the same, So we can write it as below:
\[a + b = b + d\]….. (1)
By subtracting \[b\] from both LHS and RHS side of the equation (1), we get:
\[ \Rightarrow a = d\].
Step 3: Now by solving the equations \[a + c = 13\] and \[c - a = 6\]\[{\text{(}}\because {\text{a = d)}}\], we will find the values of \[a\] and \[c\]:
Let, \[a + c = 13\]……. (2) and \[c - a = 6{\text{ }}\]… (3), By adding equation (2) and (3) we get:
\[
  a + c = 13 \\
  c - a = 6 \\
  \overline {2c = 19} \\
 \]
Now by taking \[2\] into the RHS side in the equation \[2c = 19\] and dividing it, we get:
 \[ \Rightarrow c = 9.5\]
Also, by putting the value of \[c = 9.5\] in equation (2), we calculate the value of \[a\]:
\[ \Rightarrow a + 9.5 = 13\]
By taking \[9.5\] into the RHS side and subtracting it from \[13\] we get:
\[ \Rightarrow a = 3.5\]
Step 4: Now for finding the value of the remaining variable \[b\] we will put the value of \[a = 3.5\] in the equation \[a + b = 8\] and we get:
\[ \Rightarrow 3.5 + b = 8\]
By taking \[3.5\] into the RHS side and subtracting it from \[8\] we get:
\[ \Rightarrow b = 4.5\]
Step 5: Finally, we have the required values as below:
\[\begin{array}{*{20}{l}}
  {\boxed{3.5}}& + &{\boxed{4.5}}& \Rightarrow &8 \\
   + &{}& + &{}&{} \\
  {\boxed{9.5}}& - &{\boxed{3.5}}& \Rightarrow &6 \\
   \Downarrow &{}& \Downarrow &{}&{} \\
  {13}&{}&8&{}&{}
\end{array}\]
Answer/Conclusion: \[\begin{array}{*{20}{l}}
  {\boxed{3.5}}& + &{\boxed{4.5}}& \Rightarrow &8 \\
   + &{}& + &{}&{} \\
  {\boxed{9.5}}& - &{\boxed{3.5}}& \Rightarrow &6 \\
   \Downarrow &{}& \Downarrow &{}&{} \\
  {13}&{}&8&{}&{}
\end{array}\]

Note: Students should solve these types of problems by making multiple linear equations and after that comparing them. Otherwise, we can also go for guesswork but that will take too much time and there is also a possibility of error in the answer especially since the answers are decimals.