Six is subtracted from a number. Then the result is divided by 4. The new result is added to 10 to give a final result of 30. What is the number?
Answer (2)
The unknown number is determined to be 86 by setting up a step-by-step equation based on the problem's description. Subtracting 6, dividing by 4, and adding 10 lead to the final result of 30. By solving the equation systematically, we find that the number is 86.
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Let x be the unknown number.
Form the equation: 4 x − 6 + 10 = 30 .
Solve for x : 4 x − 6 = 20 ⇒ x − 6 = 80 ⇒ x = 86 .
The number is 86 .
Explanation
Understanding the Problem Let's break down this word problem step by step to find the mystery number! We'll translate the words into a mathematical equation and then solve for the unknown.
Subtracting Six Let the unknown number be x . According to the problem, we first subtract 6 from this number, which gives us x − 6 .
Dividing by Four Next, we divide the result by 4, so we have 4 x − 6 .
Adding Ten Then, we add 10 to this new result, which gives us 4 x − 6 + 10 .
Setting up the Equation Finally, we are told that this expression equals 30. So, our equation is: 4 x − 6 + 10 = 30
Isolating the Fraction Now, let's solve for x . First, subtract 10 from both sides of the equation: 4 x − 6 = 30 − 10 4 x − 6 = 20
Removing the Fraction Next, multiply both sides of the equation by 4: x − 6 = 20 × 4 x − 6 = 80
Finding the Number Finally, add 6 to both sides of the equation to isolate x : x = 80 + 6 x = 86
The Answer Therefore, the number is 86.
Examples
Imagine you're managing a budget. You start with an unknown amount of money, spend $6, divide the remaining amount into 4 equal parts, add $10 to one of those parts, and end up with $30. This problem helps you calculate the initial amount of money you had. Understanding how to solve such problems is useful in managing personal finances, tracking expenses, and making informed financial decisions.
