Oliver bought 77 white and black balloons for a party. The number of black balloons was
25 times as many as the number of white balloons. Oliver used
13 times as many black balloons as white balloons and was left with four times as many black balloons as white balloons. How many balloons did Oliver have in the end?
|
Black (1) |
White (2) |
Make b the same. (2)x4 = (3) |
Before |
22 |
55 |
220 |
Change |
- 1 p |
- 3 p |
- 12 p |
After |
4 b |
1 b |
4 b |
Number of black balloons that Oliver bought at first = 2 u
Number of white balloons that Oliver bought at first = 5 u
Total number of balloons at first
= 2 u + 5 u
= 7 u
7 u = 77
1 u = 77 ÷ 7 = 11
Number of black balloons at first
= 2 u
= 2 x 11
= 22
Number of white balloons at first
= 5 u
= 5 x 11
= 55
22 - 1 p =
4 b --- (1)
55 - 3 p = 1 b --- (2)
(2)
x4
220 - 12 p =
4 b --- (3)
(3) = (1)
220 - 12 p = 22 - 1 p
12 p - 1 p = 220 - 22
11 p = 198
1 p = 198 ÷ 11 = 18
Number of balloons that Oliver used
= 1 p + 3 p
= 4 p
= 4 x 18
= 72
Number of balloons that Oliver had in the end
= 77 - 72
= 5
Answer(s): 5