Rael bought 140 white and black balloons for a party. The number of black balloons was ³₇ times as many as the number of white balloons. Rael used ¹₃ times as many black balloons as white balloons and was left with five times as many black balloons as white balloons. How many balloons did Rael have in the end?

	Black (1)	White (2)	Make b the same. (2)x5 = (3)
Before	42	98	490
Change	- 1 p	- 3 p	- 15 p
After	5 b	1 b	5 b

Number of black balloons that Rael bought at first = 3 u
Number of white balloons that Rael bought at first = 7 u

Total number of balloons at first
= 3 u + 7 u
= 10 u

10 u = 140

1 u = 140 ÷ 10 = 14

Number of black balloons at first
= 3 u
= 3 x 14
= 42

Number of white balloons at first
= 7 u
= 7 x 14
= 98

42 - 1 p = 5 b --- (1)
98 - 3 p = 1 b --- (2)

(2)_x5
490 - 15 p = 5 b --- (3)

(3) = (1)
490 - 15 p = 42 - 1 p
15 p - 1 p = 490 - 42 
14 p = 448

1 p = 448 ÷ 14 = 32

Number of balloons that Rael used
= 1 p + 3 p
= 4 p
= 4 x 32
= 128

Number of balloons that Rael had in the end
= 140 - 128
= 12

Answer(s): 12