## Challenge:

In the figure above, A, B, and C represent different digits. What is the value of B + C?

**A-** 8

**B-** 11

**C-** 15

**D-** 17

**E-** 18

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The correct answer is C.

In this problem, we can write a system of three equations and three variables.

Let’s review the equations.

A + B + C = 9 or 19

A + A + C = 5 or 15

A + A + A = 13 or 12

3A cannot be 13. Therefore, 3A = 12 ⇒ A = 4

We can also conclude that in the second equation:

A + A + C = 15 ⇒ 2A + C = 15 ⇒ C = 7

Or A + A + C = 16 (1 may added from the first column)

C = 6

Try different values for the first equation:

A + B + C = 9 or 19

If A = 4 and C = 6 ⇒ B = 9

If A = 4 and C = 7 ⇒ B = 8

B + C = 15

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