Question

Two types of radio valves A, B are available and two types of radios P and Q are

assembled in a small factory. The factory uses 2 valves of type A and 3 valves of

type B for the type of radio P, and for the radio Q it uses 3 valves of type A and 4

valves of type B. If the number of valves of type A and B used by the factory are

130 and 180 respectively, find out the number of radios assembled. Use Cramer’s

rule to solve.
​

Answer 1

Given :  The factory uses 2 valves of type A and 3 valves of  type B for the type of radio P, and for the radio Q it uses 3 valves of type A and 4  valves of type B. number of valves of type A and B used by the factory are  130 and 180 respectively,  

To Find : number of radios assembled Using Cramer’s  rule

Solution:

2 valves of type A and 3 valves of  type B for the type of radio P,

=> 2P  + valve A   ,  3P  = Valve B

radio Q it uses 3 valves of type A and 4 valves of type B

=> 3Q = valve A    4Q  = Valve B

2P  + 3Q  =  130

3P +  4Q =  180

$\left[\begin{array}{ccc}2&3\\3&4\end{array}\right]=2\times 4-3\times 3=-1$

$\left[\begin{array}{ccc}130&3\\180&4\end{array}\right]=130\times 4-180\times 3=-20$

P = -20/-1  = 20

$\left[\begin{array}{ccc}2&130\\3&180\end{array}\right]=2\times 180-3\times 130=-30$

Q = -30/-1  = 30

20 Radio P

30 radio Q

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