The number of blue punchers is thrice the number of yellow punchers. The number of yellow punchers is 9 more than the number of purple punchers. The total number of punchers is 121. The cost of each blue puncher is $3.90 and the cost of each purple puncher is $3.10. The total cost of all the punchers is $427.10.
- Find the number of purple punchers.
- Find the cost of a yellow puncher.
(a)
Number of purple punchers = 1 u
Number of yellow punchers = 1 u + 9
Number of blue punchers
= 3(1 u + 9)
= 3 u + 27
Total of number of punchers
= 1 u + 1 u + 9 + 3 u + 27
= 5 u + 36
5 u + 36 = 121
5 u = 121 - 36
5 u = 85
1 u = 85 ÷ 5 = 17
Number of purple punchers
= 1 u
= 17
(b)
Number of purple punchers = 17
Number of yellow punchers
= 17 + 9
= 26
Number of blue punchers
= 3 x 26
= 78
Cost of purple punchers
= 17 x 3.10
= $52.70
Cost of blue punchers
= 78 x 3.90
= $304.20
Cost of yellow punchers
= 427.10 - 304.20 - 52.70
= $70.20
Cost of 1 yellow puncher
= 70.20 ÷ 26
= $2.70
Answer(s) (a) 17; (b) $2.70
