Solve for the missing numbers in the given equations: Box + Box = 53, Box - Box = 2, where the numbers 11 and…

Question

Solve for the missing numbers in the given equations: Box + Box = 53, Box - Box = 2, where the numbers 11 and 25 are related to the first equation and 11 and 37 are related to the second.

ScanSolve AI Tutor · Accepted Answer

Let the values in the boxes be represented by variables:

\begin{bmatrix} A & B \\ C & D \end{bmatrix}

From the image, we can form the following system of equations:

Set up the equations based on the image.
1. $A + B = 53$
2. $A + C = 25$
3. $B + D = 37$
4. $C - D = 2$
Solve for $C$ and $D$ in terms of $A$ and $B$ .
From equation (2), $C = 25 - A$ .
From equation (3), $D = 37 - B$ .
Substitute these expressions for $C$ and $D$ into equation (4).
$(25 - A) - (37 - B) = 2$ $25 - A - 37 + B = 2$ $B - A - 12 = 2$ $B - A = 14 \quad (\text{Equation 5})$
Solve the system of equations (1) and (5) for $A$ and $B$ .
We have:
$A + B = 53 \quad (\text{Equation 1})$ $-A + B = 14 \quad (\text{Equation 5})$
Add Equation 1 and Equation 5:
$(A + B) + (-A + B) = 53 + 14$ $2B = 67$ $B = \frac{67}{2} = 33.5$
Substitute the value of $B$ into Equation 1:
$A + 33.5 = 53$ $A = 53 - 33.5$ $A = 19.5$
Substitute the values of $A$ and $B$ back into the expressions for $C$ and $D$ .
$C = 25 - A = 25 - 19.5 = 5.5$ $D = 37 - B = 37 - 33.5 = 3.5$
The values in the boxes are:
$\begin{bmatrix} 19.5 & 33.5 \\ 5.5 & 3.5 \end{bmatrix}$
The final answer is $A=19.5, B=33.5, C=5.5, D=3.5$ .

Solve for the missing numbers in the given equations: Box + Box = 53, Box − Box = 2, where the numbers 11 and 25 are related to the first equation and 11 and 37 are related to the second.

Answer

Step-by-step solution

Set up the equations based on the image.

Solve for $C$ and $D$ in terms of $A$ and $B$ .

Substitute these expressions for $C$ and $D$ into equation (4).

Solve the system of equations (1) and (5) for $A$ and $B$ .

Substitute the values of $A$ and $B$ back into the expressions for $C$ and $D$ .

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