Caden bought 153 red and yellow balloons for a party. The number of yellow balloons was ⁴₅ times as many as the number of red balloons. Caden used ¹₄ times as many yellow balloons as red balloons and was left with thrice as many yellow balloons as red balloons. How many balloons did Caden have in the end?

	Yellow (1)	Red (2)	Make b the same. (2)x3 = (3)
Before	68	85	255
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of yellow balloons that Caden bought at first = 4 u
Number of red balloons that Caden bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 153

1 u = 153 ÷ 9 = 17

Number of yellow balloons at first
= 4 u
= 4 x 17
= 68

Number of red balloons at first
= 5 u
= 5 x 17
= 85

68 - 1 p = 3 b --- (1)
85 - 4 p = 1 b --- (2)

(2)_x3
255 - 12 p = 3 b --- (3)

(3) = (1)
255 - 12 p = 68 - 1 p
12 p - 1 p = 255 - 68 
11 p = 187

1 p = 187 ÷ 11 = 17

Number of balloons that Caden used
= 1 p + 4 p
= 5 p
= 5 x 17
= 85

Number of balloons that Caden had in the end
= 153 - 85
= 68

Answer(s): 68