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

	White (1)	Blue (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 white balloons that Andy bought at first = 3 u
Number of blue balloons that Andy 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 white balloons at first
= 3 u
= 3 x 14
= 42

Number of blue 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 Andy used
= 1 p + 3 p
= 4 p
= 4 x 32
= 128

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

Answer(s): 12