The number of yellow punchers is twice the number of brown punchers. The number of brown punchers is 6 more than the number of purple punchers. The total number of punchers is 102. The cost of each yellow puncher is $2.60 and the cost of each purple puncher is $2.50. The total cost of all the punchers is $230.70.
- Find the number of purple punchers.
- Find the cost of a brown puncher.
(a)
Number of purple punchers = 1 u
Number of brown punchers = 1 u + 6
Number of yellow punchers
= 2(1 u + 6)
= 2 u + 12
Total of number of punchers
= 1 u + 1 u + 6 + 2 u + 12
= 4 u + 18
4 u + 18 = 102
4 u = 102 - 18
4 u = 84
1 u = 84 ÷ 4 = 21
Number of purple punchers
= 1 u
= 21
(b)
Number of purple punchers = 21
Number of brown punchers
= 21 + 6
= 27
Number of yellow punchers
= 2 x 27
= 54
Cost of purple punchers
= 21 x 2.50
= $52.50
Cost of yellow punchers
= 54 x 2.60
= $140.40
Cost of brown punchers
= 230.70 - 140.40 - 52.50
= $37.80
Cost of 1 brown puncher
= 37.80 ÷ 27
= $1.40
Answer(s) (a) 21; (b) $1.40
