The number of red punchers is twice the number of yellow punchers. The number of yellow punchers is 7 more than the number of purple punchers. The total number of punchers is 105. The cost of each red puncher is $3.70 and the cost of each purple puncher is $1.60. The total cost of all the punchers is $288.40.
- 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 + 7
Number of red punchers
= 2(1 u + 7)
= 2 u + 14
Total of number of punchers
= 1 u + 1 u + 7 + 2 u + 14
= 4 u + 21
4 u + 21 = 105
4 u = 105 - 21
4 u = 84
1 u = 84 ÷ 4 = 21
Number of purple punchers
= 1 u
= 21
(b)
Number of purple punchers = 21
Number of yellow punchers
= 21 + 7
= 28
Number of red punchers
= 2 x 28
= 56
Cost of purple punchers
= 21 x 1.60
= $33.60
Cost of red punchers
= 56 x 3.70
= $207.20
Cost of yellow punchers
= 288.40 - 207.20 - 33.60
= $47.60
Cost of 1 yellow puncher
= 47.60 ÷ 28
= $1.70
Answer(s) (a) 21; (b) $1.70
