Mary had some blue and purple marbles. If she gives away 34 blue marbles, the number of blue marbles will be 20% of the total number of marbles left. If she gives away 17 purple marbles, the number of blue marbles will be 25% of the total number of marbles left.
- How many marbles does Mary have altogether?
- What fraction of Mary's marbles is purple?
| |
Scenario 1 |
Scenario 2 |
| |
Blue |
Purple |
Blue |
Purple |
| Before |
1 u + 34 |
4 u |
1 p |
3 p + 17 |
| Change |
- 34 |
No change |
No change |
- 17 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 34 = 1 p --- (1)
4 u = 3 p + 17
4 u - 17 = 3 p --- (2)
Make p the same.
(1)
x33 u + 102 = 3 p --- (3)
(2) = (3)
4 u - 17 = 3 u + 102
4 u - 3 u = 102 + 17
1 u = 119
Number of marbles that Mary had at first
= 1 u + 34 + 4 u
= 5 u + 34
= 5 x 119 + 34
= 595 + 34
= 629
(b)
Number of purple marbles
= 4 u
= 4 x 119
= 476
Fraction of Mary's marbles that is purple
=
476629=
2837 Answer(s): (a) 629; (b)
2837 
