The number of purple punchers is twice the number of orange punchers. The number of orange punchers is 10 more than the number of green punchers. The total number of punchers is 138. The cost of each purple puncher is $4.40 and the cost of each green puncher is $3.50. The total cost of all the punchers is $516.30.
- Find the number of green punchers.
- Find the cost of a orange puncher.
(a)
Number of green punchers = 1 u
Number of orange punchers = 1 u + 10
Number of purple 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 = 138
4 u = 138 - 30
4 u = 108
1 u = 108 ÷ 4 = 27
Number of green punchers
= 1 u
= 27
(b)
Number of green punchers = 27
Number of orange punchers
= 27 + 10
= 37
Number of purple punchers
= 2 x 37
= 74
Cost of green punchers
= 27 x 3.50
= $94.50
Cost of purple punchers
= 74 x 4.40
= $325.60
Cost of orange punchers
= 516.30 - 325.60 - 94.50
= $96.20
Cost of 1 orange puncher
= 96.20 ÷ 37
= $2.60
Answer(s) (a) 27; (b) $2.60
