Simon bought 110 gold and pink balloons for a party. The number of pink balloons was ³₇ times as many as the number of gold balloons. Simon used ¹₃ times as many pink balloons as gold balloons and was left with four times as many pink balloons as gold balloons. How many balloons did Simon have in the end?

	Pink (1)	Gold (2)	Make b the same. (2)x4 = (3)
Before	33	77	308
Change	- 1 p	- 3 p	- 12 p
After	4 b	1 b	4 b

Number of pink balloons that Simon bought at first = 3 u
Number of gold balloons that Simon bought at first = 7 u

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

10 u = 110

1 u = 110 ÷ 10 = 11

Number of pink balloons at first
= 3 u
= 3 x 11
= 33

Number of gold balloons at first
= 7 u
= 7 x 11
= 77

33 - 1 p = 4 b --- (1)
77 - 3 p = 1 b --- (2)

(2)_x4
308 - 12 p = 4 b --- (3)

(3) = (1)
308 - 12 p = 33 - 1 p
12 p - 1 p = 308 - 33 
11 p = 275

1 p = 275 ÷ 11 = 25

Number of balloons that Simon used
= 1 p + 3 p
= 4 p
= 4 x 25
= 100

Number of balloons that Simon had in the end
= 110 - 100
= 10

Answer(s): 10