Solving system of equations

Question

 A machine tests solar batteries for faults. A working battery takes 3 minutes to test, but a faulty battery requires 6 minutes to detect and repair. When 24 batteries were tested it took a total of 75 minutes.

    a) Write 2 let statements for identifying the variables for this problem.

     b) Set up (write down) your system of equations. 

     

Solve the system of equations to answer the following (SHOW ALL WORK):

     c) How many batteries were faulty?

     d) How many batteries were working?

Answer 1

w+f = 24 w=number of working batteries, f = number of faulty batteries

3w + 6f = 75

multiply the 1st equation by 3 and subtract the result from the 2nd equation

3w +6f =75

3w +3f =24(3) =72

3f = 3

f =3/3 = 1 faulty battery

w =24-1= 23 working batteries