Final answer:
To solve for the sum x + y, where x:y = 2:5 and y - x = 33, set up equations representing the ratio and difference, find a common variable, solve for that variable, and then use it to determine x and y. The sum x + y equals 77.
Step-by-step explanation:
The question given is a proportion problem which involves finding the sum of two variables x and y given the ratio x:y = 2:5 and the difference y - x = 33. To find the values of x and y, we can set up two equations based on the information given. Let's solve this step-by-step:
- From the ratio x:y = 2:5, we can express x and y in terms of a common variable, say k, where x = 2k and y = 5k.
- Using the difference y - x = 33, we can substitute the expressions for x and y to get 5k - 2k = 33, simplifying to 3k = 33.
- To find k, divide both sides by 3, which gives us k = 11.
- Now we can find the values of x and y by substituting k back into the expressions for x and y, resulting in x = 2 * 11 = 22 and y = 5 * 11 = 55.
- Finally, we find x + y by adding the values together, which gives us 22 + 55 = 77.
The answer to the question is b. 77.