We have two ratios here, but they are ratios of two different numbers. This is the units and parts pattern, and this is the way I'll do it. It's not the only way.Daddy wrote:

We use units for Jane and parts for Dinah.

Jane (from 25%) 1u : 3u

Dinah (from 50%) 1p : 1p

The total number of red and blue beads doesn't change.

Red beads: 3u + 1p = 610

Blue beads: 1u + 1p = 390

[p]

[----610----]

[p]

[390]

[p] is common to top and bottom, and it adds up to 390. The top becomes

[220]

which means u = 110. Jane has 4u altogether so this is 440 beads.

a. Jane has 440 beads in the end.

Now for part b.

Dinah has p blue beads in the end

[p] is 390, and u is 110, which makes p 390 - 110 = 280

She started with 220 beads, so she received 280 - 220 = 60 beads from Jane.

b. Dinah received 60 beads from Jane.

MathWithModels