Kate spent 1 more than Lauren, and together they spent 5

Kate spent 1 more than Lauren, and together they spent 5.

Let k be the amount Kate spent, and l be the amount Lauren spent. We're given:

1. k = l + 1
2. k + l = 5

Substitute (1) into (2):
(l + 1) + l = 5

Group like terms
2l + 1 = 5

Typing this equation into our search engine, we get:
l = 2

Plug this into Equation (1), we get:
k = 2 + 1
k = 3

Kate Spent 3, and Lauren spent 2