What is the value of [tex]$x$[/tex] in the equation [tex]$2x + 3y = 36$[/tex], when [tex]$y = 6$[/tex]?
Answer (1)
Substitute y = 6 into the equation 2 x + 3 y = 36 .
Simplify the equation to 2 x + 18 = 36 .
Subtract 18 from both sides to get 2 x = 18 .
Divide by 2 to find x = 9 , so the final answer is 9 .
Explanation
Understanding the Problem We are given the equation 2 x + 3 y = 36 and the value y = 6 . Our goal is to find the value of x .
Substitution Substitute the given value of y into the equation: 2 x + 3 ( 6 ) = 36
Simplification Simplify the equation: 2 x + 18 = 36
Isolating the x term Subtract 18 from both sides of the equation: 2 x = 36 − 18 2 x = 18
Solving for x Divide both sides of the equation by 2 to solve for x : x = 2 18 x = 9
Final Answer Therefore, the value of x is 9.
Examples
Imagine you're planning a party and have a budget of $36 for food and drinks. You decide to spend $6 per guest on drinks and want to figure out how many guests you can invite if you spend a certain amount on food. This problem is similar to figuring out how many guests (x) you can invite given the equation 2 x + 3 y = 36 , where y is the cost per guest on drinks. By solving for x , you can determine the number of guests you can afford to invite while staying within your budget. This helps in real-life scenarios like budgeting, resource allocation, and planning events.
