Question

6 nuts and 5 bolts weigh 278 grams while 8 nuts and 3 bolts weigh 268 grams. Find the weigh of each nut and that of each bolt. How much do 3 nuts and 3 bolts weigh together?

Answer 1

Answer:

let weigh of each nut and each bolt be X g and Y g respectively.

According to the question, 6x+5y=278g.......(i)

and 8x+3y=268g.........(ii)

By Elimination method,

multiplying 3 in equation (i) and 5 in (ii) and then subtracting it we get,

18x+15y=834

(-)4ox+15y= 1340

-22x= -506

x=23 and y= 28

weight of 3 nuts and 3 bolts is

3x+3y

=3×23 +3×28=153g

hope this will help you

Answer 2

Step-by-step explanation:

let the weight of single nut is x gram

the weight of single bolt is y gram

so,

weight of 6 nuts will be 6x gram and

weight of 5 bolts will be 5y gram.

total weight is 278 gram

so,

6x + 5y = 278 ----(1)

similarly, second equation can be,

8x + 3y = 268 -----(2)

6x + 5y = 278. × 3

8x + 3y = 268. × 5

18x + 15y = 834

40x + 15y = 1340

-. -. -

_____________

-22x = - 506

x = 506/22

x = 23

so,

6(23) + 5y = 278

138 + 5y = 278

5y = 278-138

5y = 140

y = 140/5

y = 28

so weight of one nut is 23 gram and weight of one bolt is 28 gram

3 nut = 3(23)

3 bolts = 3 (28)

total weight = 69 + 84

= 153 gram

Hope it will help you.

Thank you.

Happy to help.