The larger integer is 28.
I'm first going to call these 2 integers n and m, where n is the larger and m is the smaller. We can now write equations based on the information they gave us:
(equation 1) n + m = 37, which tells us that the sum of the integers is 37
(equation 2) n = 3m + 1, which tells us that the larger integer is one more than 3 times the smaller.
Now we can simultaneously solve these equations, and I'm going to do this by substituting in equation 2 into equation 1:
n + m = 37
(3m + 1) + m = 37
4m + 1 = 37
- 1
4m = 364
÷ 4
m = 9
Now that we know the smaller integer is 9, we can find the larger by using equation 1:
n + m = 37
n + 9 = 37
- 9
n = 28
I hope this helps!
