Question

Jose was given this problem on his Regents Exam: "Find two consecutive odd integers where the difference of 4 times the larger and 3 times the smaller is 36." Which equation could he have used to solve this problem?

Answer 1

The correct equation to determine two consecutive odd integers where 4 times the larger minus 3 times the smaller equals 36 is 4(x + 2) - 3x = 36, which simplifies to find the integers as 28 and 30.

Step-by-step explanation:

To solve Jose's problem regarding two consecutive odd integers where the difference of 4 times the larger integer and 3 times the smaller integer is 36, we use algebra to set up an equation. Let's let the smaller odd integer be x. Because we are looking for consecutive odd integers, the next odd integer will be 2 more than x, so the larger integer will be x + 2. The problem gives us the following relationship: 4 times the larger integer minus 3 times the smaller integer equals 36. In equation form, this is 4(x + 2) - 3x = 36. Simplifying the equation, we get 4x + 8 - 3x = 36, which further simplifies to x + 8 = 36. Subtracting 8 from both sides gives us x = 28. Therefore, the two consecutive odd integers are 28 and 30.