# The ratio of the number of red beads to the number of green beads to the number of blue beads is 2 : 3 : 7. There are 150 more blue beads than red beads. How many beads are there in all? Please show work.

QUESTION POSTED AT 01/06/2020 - 03:15 PM

QUESTION POSTED AT 01/06/2020 - 03:15 PM

R = red beads

G = green beads

B = blue beads

Given:

R/2 = G/3 = B/7

B = R + 150

How many reds?

R/2 = (R+150)/7

7*R/2 = R + 150

7*R = 2*R + 300

5*R = 300

R = 60

How many blue?

B = R + 150

B = 210

How many green?

G/3 = R/2

G/3 = 60/2

G/3 = 30

G = 90

How many total?

Total = R+G+B

Total = 60+90+210

Total = 360

G = green beads

B = blue beads

Given:

R/2 = G/3 = B/7

B = R + 150

How many reds?

R/2 = (R+150)/7

7*R/2 = R + 150

7*R = 2*R + 300

5*R = 300

R = 60

How many blue?

B = R + 150

B = 210

How many green?

G/3 = R/2

G/3 = 60/2

G/3 = 30

G = 90

How many total?

Total = R+G+B

Total = 60+90+210

Total = 360

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