The sum of four times a number and seven is 27. Find the number.
Answer (1)
Represent the unknown number with a variable: x .
Formulate the equation based on the problem statement: 4 x + 7 = 27 .
Isolate the variable by subtracting 7 from both sides: 4 x = 20 .
Solve for x by dividing both sides by 4: x = 5 . The number is 5 .
Explanation
Understanding the Problem Let's break down this problem step by step!
Setting up the Equation We are given that the sum of four times a number and seven is 27. Our mission is to find that mystery number. Let's call the number x .
Forming the Equation Now, we can translate the given information into an equation. Four times the number x is 4 x , and when we add seven to that, we get 4 x + 7 . We know this sum is equal to 27, so our equation is: 4 x + 7 = 27
Isolating the Variable To solve for x , we need to isolate it on one side of the equation. First, let's subtract 7 from both sides of the equation: 4 x + 7 − 7 = 27 − 7 4 x = 20
Solving for x Now, to get x by itself, we divide both sides of the equation by 4: 4 4 x = 4 20 x = 5
Finding the Number So, the number we were looking for is 5!
Examples
Imagine you're trying to figure out how many hours you need to work this week to buy a new video game. The game costs $27, and you've already saved $7. If you earn $4 per hour, you can use this math to find out how many hours you need to work. The equation 4 x + 7 = 27 helps you determine that you need to work 5 hours to afford the game. This kind of problem-solving is useful for budgeting and planning your finances!
