The number of brown punchers is four times the number of blue punchers. The number of blue punchers is 5 more than the number of purple punchers. The total number of punchers is 109. The cost of each brown puncher is $3.30 and the cost of each purple puncher is $2.20. The total cost of all the punchers is $323.40.
- Find the number of purple punchers.
- Find the cost of a blue puncher.
(a)
Number of purple punchers = 1 u
Number of blue punchers = 1 u + 5
Number of brown punchers
= 4(1 u + 5)
= 4 u + 20
Total of number of punchers
= 1 u + 1 u + 5 + 4 u + 20
= 6 u + 25
6 u + 25 = 109
6 u = 109 - 25
6 u = 84
1 u = 84 ÷ 6 = 14
Number of purple punchers
= 1 u
= 14
(b)
Number of purple punchers = 14
Number of blue punchers
= 14 + 5
= 19
Number of brown punchers
= 4 x 19
= 76
Cost of purple punchers
= 14 x 2.20
= $30.80
Cost of brown punchers
= 76 x 3.30
= $250.80
Cost of blue punchers
= 323.40 - 250.80 - 30.80
= $41.80
Cost of 1 blue puncher
= 41.80 ÷ 19
= $2.20
Answer(s) (a) 14; (b) $2.20
