Ahmad bought 110 yellow and gold balloons for a party. The number of gold balloons was ³₇ times as many as the number of yellow balloons. Ahmad used ¹₄ times as many gold balloons as yellow balloons and was left with thrice as many gold balloons as yellow balloons. How many balloons did Ahmad have in the end?

	Gold (1)	Yellow (2)	Make b the same. (2)x3 = (3)
Before	33	77	231
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of gold balloons that Ahmad bought at first = 3 u
Number of yellow balloons that Ahmad 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 gold balloons at first
= 3 u
= 3 x 11
= 33

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

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

(2)_x3
231 - 12 p = 3 b --- (3)

(3) = (1)
231 - 12 p = 33 - 1 p
12 p - 1 p = 231 - 33 
11 p = 198

1 p = 198 ÷ 11 = 18

Number of balloons that Ahmad used
= 1 p + 4 p
= 5 p
= 5 x 18
= 90

Number of balloons that Ahmad had in the end
= 110 - 90
= 20

Answer(s): 20