Solving a word problem using a system of linear equations of the form Ax + By = C

Question

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 51 kilograms. A delivery of 6 large boxes and 5 small boxes has a total weight of 127 kilograms.

How much does each type of box weigh?

Answer 1

we have two simultaneous equations in two unknown variables, where L is weight of Large box and S is weight of small box.

(1) 2L + 3S = 51

(2) 6L + 5S = 127

3 x (1) also gives 6L which can then be eliminated by subtracting (1), hence

6L + 9S = 153

-

6L + 5S = 127

=

0L + 4S = 26

=> S = 26/4 = 6.5

substitute this in (1) to get

2L + 3(6.5) = 51

=> 2L = 51 - 19.5 = 31.5

=> L = 31.5/2 = 15.75

large box = 15.75 kg and small box = 6.5 kg

double-check: 2(15.75) + 3(6.5) = 31.5 + 19.5 = 51 and 6(15.75) + 5(6.5) = 94.5 + 32.5 = 127 as required.

Answer 2

2L + 3S = 51

6L + 5S = 127

multiply the 1st equation by 3 to get

6L + 9S = 153, subtract the 2nd equation to get

4S = 26

S = 26/4 = 6.5 kg

2L = 51 - 3(6.5) = 51 - 19.5 = 31.5

L = 31.5/2 = 15.5 kg