Penelope had a collection of 1570 red, yellow and blue marbles. After Penelope gave away 340 red marbles, the number of red marbles was 150 fewer than the number of yellow marbles. Given that the number of blue marbles was four times as many as the number of yellow marbles, how many red marbles did Penelope have at first?
| |
Red marbles |
Yellow marbles |
Blue marbles |
Total |
| Before |
1 u + 340 |
1 u + 150 |
4 u + 600 |
1570 |
| Change |
- 340 |
|
|
|
| After |
1 u |
1 u + 150 |
4 u + 600 |
|
Number of blue marbles in the end
= 4 x (1 u + 150)
= 4 u + 600
Total number of marbles at first
= 1 u + 340 + 1 u + 150 + 4 u + 600
= 6 u + 1090
6 u + 1090 = 1570
6 u = 1570 - 1090
6 u = 480
1 u = 480 ÷ 6 = 80
Number of red marbles that Penelope had at first
= 1 u + 340
= 80 + 340
= 420
Answer(s): 420
