There are some yellow and pink beads in a box. If 7 yellow beads are removed from the box, the total number of beads left will be 5 times the number of yellow beads left. If 10 pink beads are removed from the box, the total number of beads left will be 3 times the number of yellow beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Yellow beads |
Pink beads |
Yellow beads |
Pink beads |
Before |
1 u + 7 |
4 u |
1 p |
2 p + 10 |
Change |
- 7 |
|
|
- 10 |
After |
1 u |
4 u |
1 p |
2 p |
Number of pink beads in the end for Case 1
= 5 u - 1 u
= 4 u
Number of yellow beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of yellow beads at first is the same for Case 1 and Case 2.
The number of pink beads at first is also the same for Case 1 and Case 2.
1 u + 7 = 1 p --- (1)
4 u = 2 p + 10
4 u - 10 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 14 =
2 p --- (3)
(2) = (3)
4 u - 10 = 2 u + 14
4 u - 2 u = 14 + 10
2 u = 24
1 u = 24 ÷ 2 = 12
Number of beads in the box
= (1 u + 7) + 4 u
= 5 u + 7
= (5 x 12) + 7
= 60 + 7
= 67
Answer(s): 67