When 5 is added to six times a number, the result is 35. What is the number?
The correct answer and explanation is:
Let’s solve the problem step-by-step:
Problem:
When 5 is added to six times a number, the result is 35. Find the number.
Step 1: Define the variable
Let the unknown number be x.
Step 2: Translate the words into an equation
- “Six times a number” means 6×x=6×6 \times x = 6x.
- “5 is added to six times a number” means 6x+56x + 5.
- “The result is 35” means the total equals 35.
So the equation is: 6x+5=356x + 5 = 35
Step 3: Solve the equation
Subtract 5 from both sides to isolate the term with xx: 6x+5−5=35−5 ⟹ 6x=306x + 5 – 5 = 35 – 5 \implies 6x = 30
Divide both sides by 6 to solve for xx: x=306=5x = \frac{30}{6} = 5
Final Answer:
5\boxed{5}
Explanation (300 words):
This problem is a classic example of forming and solving a linear equation based on a word problem. The key to solving such problems is to carefully translate the words into a mathematical expression, assign variables correctly, and then use algebraic manipulation to find the value of the unknown.
In this problem, the phrase “six times a number” translates directly to multiplying an unknown variable (which we call xx) by 6, resulting in 6x6x. Next, the phrase “when 5 is added to six times a number” tells us to add 5 to this product, giving the expression 6x+56x + 5.
The phrase “the result is 35” sets this entire expression equal to 35, leading to the equation 6x+5=356x + 5 = 35.
To find xx, we isolate it by first removing the constant term on the left side. Subtracting 5 from both sides keeps the equation balanced and leaves 6x=306x = 30. Dividing both sides by 6 removes the coefficient of xx, leaving us with x=5x = 5.
Thus, the number we were looking for is 5. This solution is easily verified by plugging x=5x = 5 back into the original expression: 6×5+5=30+5=356 \times 5 + 5 = 30 + 5 = 35, which matches the problem statement perfectly.
This example highlights the power of algebra in converting real-world problems into solvable mathematical expressions, emphasizing the importance of understanding the relationship between words and numbers.