Let the number of red beads be r.
Let the number of white beads be w.
r + w = 50
r = 6w + 1
Substitute 6w + 1 in for r in the first equation.
6w + 1 + w = 50
7w + 1 = 50
7w = 49
w = 7
She has 7 white beads.
Now we use the first equation to find the number of red beads.
r + w = 50
r + 7 = 50
r = 43
She has 43 red beads.
