Question

Question 22 a fruit company delivers its fruit in two types of boxes: large and small. a delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. a delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. how much does each type of box weigh

Answer 1

Let L be the weight of a large box and S be the weight of a small box.  So we can set up two equations: 2L + 3S = 834L + 8S = 197 Solve for L or S in one of the equations and substitute it into the other equation and find the other unknown. 2L = 83 - 3SL = (83 - 3S)/2 4(83 - 3S)/2 + 8S = 197166 - 6S + 8S = 1972S = 31
S = 15.5 kg
L = (83 - 3(15.5))/2 = 18.25 kg

Answer 2

Set this up as a system of equations.  The first will be the 2 large boxes plus the 3 small boxes weigh 83 kg, the second will be the 4 large boxes plus the 8 small weigh 197 kg.  2L + 3s = 83  and   4L + 8s = 197.  Solve one of them for either variable.  Let's solve the second one for L:  L = -2s + 49.25.  Sub that value of L into the first equation: 2(-2s + 49.25) + 3s = 83.  Distribute through the parenthesis to get -4s + 98.5 + 3s = 83.  Combine like terms to get -s =-15.5.  or s = 15.5.  So a small box weights 15.5 kg.  A large box is -2(15.5) + 49.5, which is 18.5 kg.