The number of brown punchers is twice the number of blue punchers. The number of blue punchers is 10 more than the number of purple punchers. The total number of punchers is 114. The cost of each brown puncher is $2.80 and the cost of each purple puncher is $3.50. The total cost of all the punchers is $333.90.
- 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 + 10
Number of brown punchers
= 2(1 u + 10)
= 2 u + 20
Total of number of punchers
= 1 u + 1 u + 10 + 2 u + 20
= 4 u + 30
4 u + 30 = 114
4 u = 114 - 30
4 u = 84
1 u = 84 ÷ 4 = 21
Number of purple punchers
= 1 u
= 21
(b)
Number of purple punchers = 21
Number of blue punchers
= 21 + 10
= 31
Number of brown punchers
= 2 x 31
= 62
Cost of purple punchers
= 21 x 3.50
= $73.50
Cost of brown punchers
= 62 x 2.80
= $173.60
Cost of blue punchers
= 333.90 - 173.60 - 73.50
= $86.80
Cost of 1 blue puncher
= 86.80 ÷ 31
= $2.80
Answer(s) (a) 21; (b) $2.80
