The number of brown punchers is thrice the number of purple punchers. The number of purple punchers is 7 more than the number of red punchers. The total number of punchers is 138. The cost of each brown puncher is $3.80 and the cost of each red puncher is $3.20. The total cost of all the punchers is $438.70.
- Find the number of red punchers.
- Find the cost of a purple puncher.
(a)
Number of red punchers = 1 u
Number of purple punchers = 1 u + 7
Number of brown punchers
= 3(1 u + 7)
= 3 u + 21
Total of number of punchers
= 1 u + 1 u + 7 + 3 u + 21
= 5 u + 28
5 u + 28 = 138
5 u = 138 - 28
5 u = 110
1 u = 110 ÷ 5 = 22
Number of red punchers
= 1 u
= 22
(b)
Number of red punchers = 22
Number of purple punchers
= 22 + 7
= 29
Number of brown punchers
= 3 x 29
= 87
Cost of red punchers
= 22 x 3.20
= $70.40
Cost of brown punchers
= 87 x 3.80
= $330.60
Cost of purple punchers
= 438.70 - 330.60 - 70.40
= $37.70
Cost of 1 purple puncher
= 37.70 ÷ 29
= $1.30
Answer(s) (a) 22; (b) $1.30
