Math  /  Algebra

Question(5.) The sum of two numbers is 54 . Let xx represent the smaller number, and let x+2x+2 represent the larger number. Write and solve an equation to determine the numbers. Check your solution.

Studdy Solution

STEP 1

1. The sum of two numbers is 54.
2. Let x x represent the smaller number.
3. The larger number is represented by x+2 x + 2 .
4. We need to write and solve an equation to find the numbers.
5. We will check the solution to ensure accuracy.

STEP 2

1. Define the relationship between the numbers.
2. Write an equation based on the given information.
3. Solve the equation for x x .
4. Find the values of both numbers.
5. Check the solution to verify correctness.

STEP 3

Define the relationship between the numbers.
The smaller number is x x and the larger number is x+2 x + 2 .

STEP 4

Write an equation based on the given information.
Since the sum of the two numbers is 54, we can write:
x+(x+2)=54 x + (x + 2) = 54

STEP 5

Simplify and solve the equation for x x .
Combine like terms:
2x+2=54 2x + 2 = 54
Subtract 2 from both sides to isolate the term with x x :
2x=542 2x = 54 - 2 2x=52 2x = 52
Divide both sides by 2 to solve for x x :
x=522 x = \frac{52}{2} x=26 x = 26

STEP 6

Find the values of both numbers.
The smaller number is x=26 x = 26 .
The larger number is x+2=26+2=28 x + 2 = 26 + 2 = 28 .

STEP 7

Check the solution to verify correctness.
The sum of the numbers should be 54:
26+28=54 26 + 28 = 54
Since the sum is correct, the solution is verified.

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