**Half of the difference between two numbers is 2. The sum of the greater and twice the smaller number is 13. Find the numbers.**

**Ans:**

**Step 1:**

Let the numbers be x and y.

Here, x is the greater number and y is the smaller number.

**Step 2:**

by 1st condition, we get:

½ (x- y) = 2

∴ x – y = 4………….. (i)

**Step 3:**

by 2nd condition, we get:

x + 2 y = 13 ………… (ii)

**Step 4:**

By subtracting equations (i) from equation (ii), we get:

(x + 2y) – (x – y) = 13 – 4

∴ x + 2y – x + y = 9

∴ 3 y = 9

**∴ y = 3**

**Step 5:**

By substituting value of y in equation (i), we get:

x = 4 + y

∴ x = 4 + 3

**∴ x = 7**

**Therefore, the numbers are 7 and 3.**

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