### Question:

What are the values of A, B, C, and D?

**(An image is shown after the explanation)**

### Explanation

Attention, math enthusiasts! Brace yourselves for an intriguing puzzle that will put your problem-solving skills to the test. Get ready to dive into the world of simultaneous equations and unlock the secrets of the four mysterious boxes.

In this mind-boggling quiz, we are presented with four boxes, two at the top and two at the bottom. Let’s assign each box a letter to keep track of them: the top left box will be A, the top right box will be B, the bottom left box will be C, and the bottom right box will be D.

Now, here’s the challenge: We need to find the values inside these boxes that satisfy the given conditions. Let’s take a closer look at the clues:

Condition 1: A + B = 8 Condition 2: C – D = 6 Condition 3: A + C = 13 Condition 4: B + D = 8

**To crack this puzzle, we’ll employ a popular problem-solving technique called substitution. Let’s walk through the steps together.**

Starting with Condition 1, we can isolate B by subtracting A from both sides: B = 8 – A. This gives us a way to express B in terms of A.

Next, we substitute this expression for B into Condition 4: (8 – A) + D = 8. By simplifying this equation, we discover that D is equal to A.

Now, armed with the knowledge that D is equal to A, we substitute D with A in Condition 2: C – A = 6. This creates a system of equations involving A and C.

To solve this system, we add Condition 3 (A + C = 13) to Condition 2 (C – A = 6). Combining the equations, we find that 2C equals 19 when simplified.

Dividing both sides of the equation by 2, we determine that C is equal to 9.5. With this valuable information, we can substitute the value of C back into Condition 3 and solve for A, revealing that A is 3.5.

With A and C figured out, we move on to Condition 1 and substitute the known values to find B: 3.5 + B = 8. Subtracting 3.5 from both sides, we deduce that B is 4.5.

Finally, we return to Condition 2 and replace A with 3.5: 9.5 – D = 6. Subtracting 9.5 from both sides, we conclude that D is 3.5.

After successfully solving the simultaneous equations, we have uncovered the values hidden within the boxes: A = 3.5 B = 4.5 C = 9.5 D = 3.5

Congratulations, puzzle solvers! You have navigated the twists and turns of simultaneous equations to unravel the mystery of the four boxes. Your mathematical prowess shines brightly. Keep challenging your mind and embracing the thrill of solving perplexing puzzles like this one.