A fruit company delivers it’s fruit and two types of boxes large and small delivery of five large boxes and six more boxes has a total weight of 175 kg a delivery of three large boxes and two small boxes has a total weight of 83 kg how much does each type of box weigh ?
Let a be the weight of Large box
and Let b be the weight of Small box
therefore, the equation will be
=> 5a + 6b = 175kg ----------(1)
3a + 2b = 83kg ------(2)
now, Multiplying equation (2) by 3 on both sides
we get,
3a*3 + 2b*3 = 83*3
=> 9a + 6b = 249 -----(3)
now subtracting equ. 2 and equ. 3
we get,
5a +
6b= 175(-) 9a(-)+
6b=(-)249-------------------------
=> -4a = -74
a = -74/-4
--------------
/ a= 18.5 /
-------------
Therefore the weight of the large box is 18.5 kg
now ,
subtituting value of a in equation b
we get,
3a + 2b = 83
=> 3*(18.5) + 2b = 83
55.5 + 2b = 83
2b = 83 - 55.5
2b = 27.5
b = 27.5 / 2
-----------------
/ b = 13.75 /
-----------------
Therefore the weight of the small box is 13.75kg
and the weight of large box is 18.5kg