Answer: see below
Explanation:
Set up two equations, one for each scenario
88w + 21b = 5840
84w + 82b = 9044
Use one equation and isolate one of the variables. We'll isolate w in the first equation.
88w + 21b = 5840
88w = 5840 - 21b
w = (5840 - 21b)/88
Then substitute that into the second equation.
84w + 82b = 9044
42w + 41b = 4522 (simplified)
42((5840 - 21b)/88) + 41b = 4522
21((5840 - 21b)/44) + 41b = 4522 (simplified)
(122640 - 441b)/44 + 1804b/44 = 4522
(122640 - 441b + 1804b)/44 = 4522
122640 + 1363b = 198968
1363b = 76328
b = 56
Now that we know belts are $56, we can substitute that back into any equation and solve for w.
w = (5840 - 21b)/88
w = (5840 - 21(56))/88
w = (5840 - 1176)/88
w = 4664/88
w = 53