Need help with math.

A : B = 2 : 3 B : C = 4 : 5. Now, to find A : B : C, we need to make the value of B equal in A : B ratio and B : C ratio. Here, Value of B in A : B ratio is 3; and B : C ratio is 4. LCM of 3 and 4 is 12. Therefore, we multiply 4 to the first ratio and 3 to the second ratio. A : B = 2 × 4 : 3 × 4 A : B = 8 : 12 Also, B : C = 4 × 3 : 5 × 3 B : C = 12 : 15 Now, we can combine A : B and B : C. A : B : C = 8 : 12 : 15.

Step-by-step explanation:

the  12 : 15

             a = 60

             b = 80, and

             c = 100

Step-by-step explanation:

Be patient, this requires a few tedious steps.

We can take the first expression and pick one of the unknowns, I'll choose a, and rearrange the expressions such that a is expressed as a function of b and c.

Since:

a/3 = b/4 = c/5

We can separate out the values of b and c and express them as a function of a.

For example, a/3 = b/4 can be rewritten as

a/3 = b/4

4a = 3b

b = (4/3)a

When we're ready, we can substitute this value for b in the second equation, thereby eliminating b from the 2nd equation.

First, let's do the same for c:

a/3 = c/5

5a = 3c

c = (5/3)a

Now we can use the values for both b and c expressed only with "a" as the variable.  Use these values for b ((4/3)a) and c ((5/3)a) in the second equation:

240 - b = a + c

240 - (4/3)a = a + (5/3)a

240 = = a + (5/3)a +  (4/3)a

240 = (3/3)a + (5/3)a + (4/3)a

240 = (12/3)a

a = (240)*(3/12)

a = 60

Now that we have a, we can use the relationships we established at the start:

b = (4/3)a

b = (4/3)(60)

b = 80

c = (5/3)a

c = (5/3)(60)

c = 100

==

Summary

             a = 60

             b = 80, and

             c = 100

Do these work?

Check the numbers for 240 - b = a + c

                                    240 - 80 = 60 + 100 ?  

                                               160 = 160                          YES

And does  a/3 = b/4 = c/5?

                                 a/3 =  60/3 = 20

                                 b/4 =  80/4 = 20

                                 c/5 = 100/5 = 20                             YES