Question

Given that 8 bolts and 6 nuts weigh 138grams and 3 bolts and 5 nuts weigh 71 grams. Find the weight of;(a)one bolt and one nut (b)4 bolts and 3 nuts (c)11 bolts and 11 nuts​

Answer 1

Answer:

(a) Weight of a bolt = 12 grms and weight of a nut is 7 gms. Weight of one bolt and one nut = 12 + 7 = 19 gms

(b) 69 gms

(c) 209 gms

Step-by-step explanation:

This problem relates to solution of 2 unknowns using simultaneous equations.

Let B be the weight of a single bolt and N be the weight of a single nut

Since 8 bolts and 6 nuts weigh 138 grams we get one of the equations as

8B + 6N = 138    (1)

The second equation in the unknowns is

3B + 5N = 71  (2)

To solve, we eliminate one of the unknowns by making its coefficients the same and subtracting one from the other

Multiplying (1) by 5 ===>   40B + 30N = 690   (3)

Multiplying (2) by 6 ===>  18B + 30N = 426    (4)

(3) - (4) eliminates the N variables and yields

22B = 264   ==> B = 264/22 ==> B = 12

So the weight of a single bolt is 12 grams

We can find the weight of a single nut by substituting this value of B into any of the equations (1), (2), (3) or (4) and solving for N. Let's use equation (2)

3(12) + 5N = 71 ==>  36 + 5N = 71 ==> 5N = 71-36 = 35 ==>  N= 7

So the weight of a single nut is 7 grams

Weight of one bolt and one nut is the sum of the above individual weights = 12 + 7 = 19 gms

To solve (b) and (c) we could set up two other equations and plug in values for B and N

(b) 4B + 3N = 4.12 + 3.7 = 69
However, an alternate way is to perceive that 4B + 3N is exactly half of 8B + 6N so the value of that must be 138/2 = 69

(c) If we add both equations (1) and (2), we get

11B + 11N = 138 + 71 = 209 which is the equation for the total weight of 11 bolts and 11 nuts