College Algebra word problem

Question

Find the smallest values for a and b so that 24b = 28a

 

a- _____________

 

b- _____________

Answer 1

Lets rearrange the equation as

 

24b - 28a = 0

 

 

We factor the equation by taking out the GCF.  GCF is 4.

 

4(6b - 7a) = 0

 

 

Divide 4 on both sides of equation.

 

6b - 7a = 0

 

 

If we multiply the coefficients of a and b by their reciprocals, we obtain the value of 1. Therefore

 

a = 1/7

b = 1/6

 

 

Let check this theory by plugging these values.

 

24b = 28a

 

24(1/6) = 28(1/7)

     4     =    4