# Question

Janice has some blue and green marbles. If she uses 30 blue marbles, the number of blue marbles left will be 20% of the total number of marbles left. If she uses 60 green marbles, the number of blue marbles left will be 25% of the total number of marbles left.

a) How many beads does Janice have altogether?

B) what fraction of jolene’s marbles are blue?

(a)
blue marbles : 10u
green marbles : 10p

If she uses 30 blue marbles, the number of blue marbles left will be 20% of the total number of marbles left,
10u – 30 = 20% x (10u – 30 + 10p) = 2u – 6 + 2p
8u – 24 = 2p
1p = 4u – 12

If she uses 60 green marbles, the number of blue marbles left will be 25% of the total number of marbles left,
10u = 25% x (10u + 10p – 60) = 2.5u + 2.5p – 15

7.5u = 2.5p – 15 = 2.5 x (4u – 12) – 15 = 10u – 45
2.5u = 45
1u = 18
1p = 4 x 18 – 12 = 60
10u + 10p = 180 + 600 = 780

(b)
180/780 = 3/13

Ans : (a) 780 marbles; (b) 3/13

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Blue           Green             Total

Before        1u + 30             4u              5u + 30

Change               -30

After               1u                    4u                5u

Blue           Green             Total

Before                1p            3p + 60

Change                                    -60

After                   1p                    3p               4p

1p = 1u + 30

4u = 3p + 60

4u = 3u + 90  + 60

1u = 150

Total = 5u + 30 = 780

Fraction which is blue = 180/780 = 3/13