Question

two types of boxes a b are to be placed in a truck having capacity of 10 tons when 150 boxes of type a and 100 boxes of type b are loaded in the truck it weighs 10 tons but when 260 boxes of type a are loaded in the truckit can still accomodate 40 boxes of type b so that it is fully loaded find the weight of each type of box

Answer 1

Hi ,

Let us assume ,

weight of each type A box = x tons

weight of each type B box = y tons

according to the problem given ,

150 boxes of typeA and 100 boxes of type B

boxes Weighs 10 tons

15x + 100y = 10

15x + 10y = 1 ----( 1 )

260 boxes of type A and 40 boxes of type B

boxes Weighs = 10 tons

260x + 40y = 10

26x + 4y = 1 ---( 2 )

multiply equation ( 1 ) with 2 and equation

( 2 ) with 5 , we get

30x + 20y = 2 ----( 3 )

130x + 20y = 5 ----( 4 )

subtract equation ( 3 ) from equation ( 4 ),

we get

100x = 3

x = 3/100 tons

put x value in equation ( 3 ) we get ,

y = 11/200 tons

Therefore ,

weight of each type A box = x

x = 3/100 tons

x = ( 3/100 ) × 1000 kg

x = 30 kg

weight of each type B box = y

y =[11/200 ] tons

y = ( 11/200 ) × 1000 kg

y = 55 kg

I hope this helps you.

: )

Answer 2

heya..!!!!

let the of weight of each A types box = x

and the mass of each B types of box = y

according to question,

case--(1)

150 boxes of type A and 100 boxes of type

B weighs =10 tons 

=> 150x + 100y = 10

=> 15x + 10y = 1--------(1)

case--(1)

260 boxes of type A and 40 boxes of type B 

weighs = 10 tons

=> 260x + 40y = 10

=> 26x + 4y = 1-----(2)

from--(1) and--(2)
multiply by (2) in--(1) and by (2)in --(2)

30x + 20y = 2
130x + 20y = 5
(-)____(-)____(-)
—————————
-100x = -3

=> x = 3/100tons [ put in--(1)]

we get,

15(3/100) + 10y = 1

=> 9/20 + 10y = 1

=> (9 + 200y)/20 = 1

=> 9 + 200y = 20

=> 200y = 11

=> y = 11/200tons

weight of each A type of box = 3/100 × 1000kg

=> 30kg

AND,

the weight of each B type of box = 11/200 × 1000kg

=> 11×5 = 55kg

hope it's help you