Select the correct answer.
The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults, which proportion and solution represent this situation?
[tex]\frac{2}{5}=\frac{x+12}{x} ; x=20[/tex]
[tex]\frac{2}{5}=\frac{x+12}{x} ; x=4[/tex]
[tex]\frac{2}{5}=\frac{x}{x+12} ; x=8[/tex]
[tex]\frac{2}{5}=\frac{x}{x+12} ; x=4[/tex]
Answer (2)
Let x represent the number of adults.
Express the number of students as x + 12 .
Set up the proportion 5 2 = x + 12 x .
Solve for x , which gives x = 8 . The correct answer is 8 .
Explanation
Understanding the Problem Let's analyze the problem. We are given that the ratio of adults to students is 2:5. We are also told that there are 12 more students than adults. We need to find the proportion that represents this situation and solve for the number of adults.
Setting up the Proportion Let x be the number of adults. Then, since there are 12 more students than adults, the number of students is x + 12 . The ratio of adults to students is given as 2 to 5, which can be written as 5 2 . Therefore, we can set up the proportion as students adults = x + 12 x . This gives us the equation 5 2 = x + 12 x .
Solving for x Now, we solve the proportion for x . Cross-multiplying, we get 2 ( x + 12 ) = 5 x . Expanding the left side, we have 2 x + 24 = 5 x . Subtracting 2 x from both sides, we get 24 = 3 x . Dividing both sides by 3, we find x = 8 .
The Answer Therefore, the correct proportion is 5 2 = x + 12 x , and the solution is x = 8 .
Examples
Understanding ratios and proportions is crucial in many real-life situations. For example, when baking, you might need to adjust ingredient quantities based on a specific ratio. If a recipe calls for a flour-to-sugar ratio of 3:1 and you want to use 6 cups of flour, you can set up a proportion to find out how much sugar you need. Similarly, in construction, ratios are used to determine the correct mixture of cement, sand, and gravel for concrete. Knowing how to set up and solve proportions helps ensure the final product meets the required specifications.
The correct proportion representing the situation is 5 2 = x + 12 x with a solution of x = 8 . Therefore, the number of adults is 8. The answer corresponds to option: 5 2 = x + 12 x ; x = 8
;
