# Mathematics Challenge

**Problem:**

1. If 2x + y = 13 and x + 2y = 11, what is the value of x + y?

2. Determine the units digit of the integer equal to 9 + 9^{2} + 9^{3} + 9^{4}.

(The units digit of an integer is its rightmost digit. For example, the units digit of

the integer 1234 is 4.)

Answer ?

**Solution 1**

Adding the two equations gives (2x + y) + (x + 2y) = 13 + 11 or 3x + 3y = 24.

Thus, x + y = 1/3(24) = 8.

**Solution 2**

We note that 9 + 9^{2} + 9^{3}+ 9^{4} = 9(1 + 9^{1}) + 9^{3}(1 + 9^{1}) = (9 + 9^{3})(1 + 9) = 10(9 + 9^{3}).

Therefore, 9 + 9^{2} + 9^{3} + 9^{4} is an integer that is divisible by 10, so its units digit is 0.

### Comments

**One Response to “Mathematics Challenge”**

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let a and b be real numbers such that a>b>c. determine the least possible value of

a + 1/b(a-b)

please send your answer to nasrul.coral@gmail.com