Let,
A = the number of hours factory A should operate
B = the number of hours factory B should operate
FOCUSING IN ORDER ONE:
For Jelly Beans,
400A + 150B = 12,600 (Equation 1)
For Chocolates:
100A + 350B = 9,400 (Equation 2)
Apply the Substitution Method:
100A + 350B = 9,400
100A = 9,400 - 350B
(100A = 9,400 - 350B) ÷ 100
A = 94 - 3.5B (Equation 3)
Substitute Eq. 3 to Eq. 1
400A + 150B = 12,600
(400A + 150B = 12,600) ÷ 400
A + 0.375B = 31.5
94 - 3.5B + 0.375 = 31.5
-3.125B = 31.5 - 94
-3.125B = -62.5
(-3.125B = -62.5) ÷ -3.125
B = 20
Plugin B = 20 in Equation 2 to find A.
100A + 350B = 9,400
100A + 350(20) = 9,400
100A + 7,000 = 9,400
100A = 9,400 - 7,000
100A = 2,400
(100A = 2,400) ÷ 100
A = 24
Therefore, for Order 1;
Factory A should operate for 24 hours
Factory B should operate for 20 hours