For each of the following, define a variable for the unknown, write and solve an equation, then answer the question that was asked. ONLY ONE VARIABLE SHOULD BE USED FOR EACH.
a. Three times a number decreased by four is equal to twenty-five.
Answer (2)
We defined the variable as x , wrote the equation as 3 x − 4 = 25 , and solved it to find x = 3 29 . This indicates that the unknown number is approximately 9.67. Therefore, three times this number decreased by four equals twenty-five.
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Define the variable: Let x be the unknown number.
Write the equation: Translate the problem into the equation 3 x − 4 = 25 .
Solve for x : Add 4 to both sides to get 3 x = 29 , then divide by 3 to find x = 3 29 .
State the solution: The number is 3 29 .
Explanation
Understanding the Problem Let's break down this problem step by step so we can solve it together!
Setting up the Variable We need to find a number that satisfies a specific condition. The problem tells us that if we multiply this number by three and then subtract four, the result is twenty-five.
Writing the Equation Let's use the variable x to represent the unknown number we're trying to find.
Solving the Equation Now, let's translate the words into a mathematical equation. "Three times a number" can be written as 3 x . "Decreased by four" means we subtract 4, so we have 3 x − 4 . The problem states this is "equal to twenty-five", so our complete equation is: 3 x − 4 = 25
Isolating the Variable To solve for x , we need to isolate it on one side of the equation. First, let's add 4 to both sides of the equation to get rid of the -4 on the left side: 3 x − 4 + 4 = 25 + 4 3 x = 29
The Answer Now, to get x by itself, we divide both sides of the equation by 3: 3 3 x = 3 29 x = 3 29
Final Answer So, the unknown number is 3 29 , which is approximately 9.67.
Examples
Imagine you're baking cookies and need to adjust a recipe. If the original recipe calls for a certain amount of sugar, but you want to triple the recipe and then remove a small portion (like 4 tablespoons), you can use this type of equation to figure out the new amount of sugar needed so that the final sweetness is equivalent to 25 units of sweetness. This kind of problem helps in scaling recipes or adjusting ingredient quantities while maintaining the desired outcome.
