Twice a number increased by 17 is 47. Find the number.
The correct answer and explanation is:
Let the unknown number be represented by xx. The problem states that twice the number increased by 17 is equal to 47. This relationship can be written as an equation: 2x+17=472x + 17 = 47
The goal is to find the value of xx.
Step 1: Isolate the term involving xx
To solve for xx, first subtract 17 from both sides of the equation. This will eliminate the 17 on the left side: 2x+17−17=47−172x + 17 – 17 = 47 – 17
Simplifying both sides: 2x=302x = 30
Step 2: Solve for xx
Now, to isolate xx, divide both sides of the equation by 2: 2×2=302\frac{2x}{2} = \frac{30}{2}
Simplifying: x=15x = 15
Step 3: Verify the solution
To verify that the solution is correct, substitute x=15x = 15 back into the original equation: 2(15)+17=472(15) + 17 = 47
Simplifying: 30+17=4730 + 17 = 47
Since both sides of the equation are equal, the solution x=15x = 15 is correct.
Conclusion
The number is 15. This problem involves setting up a simple linear equation based on the given relationship and then solving for the unknown number. The process included isolating the variable on one side of the equation and solving through basic algebraic steps.