The number of purple punchers is thrice the number of orange punchers. The number of orange punchers is 5 more than the number of red punchers. The total number of punchers is 130. The cost of each purple puncher is $4.40 and the cost of each red puncher is $2.40. The total cost of all the punchers is $471.30.
- Find the number of red punchers.
- Find the cost of a orange puncher.
(a)
Number of red punchers = 1 u
Number of orange punchers = 1 u + 5
Number of purple punchers
= 3(1 u + 5)
= 3 u + 15
Total of number of punchers
= 1 u + 1 u + 5 + 3 u + 15
= 5 u + 20
5 u + 20 = 130
5 u = 130 - 20
5 u = 110
1 u = 110 ÷ 5 = 22
Number of red punchers
= 1 u
= 22
(b)
Number of red punchers = 22
Number of orange punchers
= 22 + 5
= 27
Number of purple punchers
= 3 x 27
= 81
Cost of red punchers
= 22 x 2.40
= $52.80
Cost of purple punchers
= 81 x 4.40
= $356.40
Cost of orange punchers
= 471.30 - 356.40 - 52.80
= $62.10
Cost of 1 orange puncher
= 62.10 ÷ 27
= $2.30
Answer(s) (a) 22; (b) $2.30
