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## Solve Math Problems Step by Step

### Solved Examples

**Question 1:**Find four consecutive integers whose sum is 226.

**Solution:**

Let us consider four consecutive integers

First Integer = x

Second Integer = x + 1

Third Integer = x + 2

Fourth Integer = x + 3

Sum of four consecutive integers = 226

=> x + (x + 1) + (x + 2) + ( x + 3) = 226

=> x + x + 1 + x + 2 + x + 3 = 226

=> 4x + 6 = 226

Subtract 6 from both sides

=> 4x + 6 - 6 = 226 - 6

=> 4x = 220

Divide each side by 4

=> x = $\frac{220}{4}$

=> x = 55, first number

Second Integer = x + 1 = 55 + 1 = 56

Third Integer = x + 2 = 55 + 2 = 57

Fourth Integer = x + 3 = 55 + 3 = 58

Hence, three consecutive integers are, 55, 56, 57, 58.

First Integer = x

Second Integer = x + 1

Third Integer = x + 2

Fourth Integer = x + 3

Step 1:Step 1:

Sum of four consecutive integers = 226

=> x + (x + 1) + (x + 2) + ( x + 3) = 226

=> x + x + 1 + x + 2 + x + 3 = 226

=> 4x + 6 = 226

Subtract 6 from both sides

=> 4x + 6 - 6 = 226 - 6

=> 4x = 220

Divide each side by 4

=> x = $\frac{220}{4}$

=> x = 55, first number

Step 2:Step 2:

Second Integer = x + 1 = 55 + 1 = 56

Third Integer = x + 2 = 55 + 2 = 57

Fourth Integer = x + 3 = 55 + 3 = 58

Hence, three consecutive integers are, 55, 56, 57, 58.

**Question 2:**Divide 500 dollars between Stefy, Amera, Jacson so that Stefy has 50 dollars more than Jacson and Amera has 45 more than Jacson.

**Solution:**

**Step 1:**

Let Jacson has dollars = x

Therefore Stefy has dollars = 50 + x

and Amren has dollars = 45 + x

Total amount = 500 dollars

Step 2:

Step 2:

Divide 500 dollars between Stefy, Amera, Jacson

=> x + (50 + x) + (45 + x) = 500

=> x + 50 + x + 45 + x = 500

=> 3x + 95 = 500

=> 3x = 500 - 95

=> 3x = 405

Divide each side by 3

=> x = $\frac{405}{3}$

=> x = 135

Step 3:

Step 3:

Jacson has = 135 dollars.

Stefy has = 50 + x = 50 + 135 = 185 dollars

and Amren has = 45 + x = 45 + 135 = 180 dollars.

Hence, Stefy, Amera, Jacson has 185 dolars, 180 dollars and 135 dollars respectively.

**Question 3:**The sum of two numbers is 90 and their ratio is 2:3. Find the numbers.

**Solution:**

**Step 1:**

Let the number be x

Second number = 90 - x (because the sum of two numbers is 90)

**Step 2:**

According to the problem:

Ratio of two numbers = $\frac{2}{3}$

=> $\frac{x}{90 - x} = \frac{2}{3}$

=> 3x = 2(90 - x)

=> 3x = 180 - 2x

=> 3x + 2x = 180

=> 5x = 180

Divide each side by 5

=> $\frac{5x}{5} = \frac{180}{5}$

=> x = 36

Hence the number be 36. answer