# larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?

Discussion in 'Calculator Requests' started by math_celebrity, Oct 20, 2021.

1. ### math_celebrityAdministratorStaff Member

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?

Declare variables for the 2 numbers:
• Let l be the larger number
• Let s be the smaller number

We're given two equations:
1. l = s + 4
2. l + s = 40
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4

Cancel the 4's and we get:
s = l - 4

Our given equations are now:
1. s = l - 4
2. l + s = 40
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40

Grouping like terms for l, we get:
2l - 4 = 40

Add 4 to each side:
2l - 4 + 4 = 40 + 4

Cancelling the 4's on the left side, we get
2l = 44

Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2

Cancel the 2's on the left side and we get:
l = 22