Question

A piece of ribbon is cut into 3 different pieces A, B and C. The ratio of the length of A to the length of B is 3 : 4. The ratio of the length of B to that of C is 8 : 9. If C is 6m longer than A, what is the total length of the ribbon?

Answer 1

Explanation:

`(A)/(B):(3)/(4)` and
`(B)/(C): (8)/(9)` and we are told that C is 6cm longer than A. That means that C = A + 6.

We are going to cross multiply each one of those ratios. The first one gives us

4A = 3B and the second one gives us

9B = 8C. But since C = A + 6, then

9B = 8(A + 6) and

9B = 8A + 48 and

Now we will solve the first equation above for A:

If 4A = 3B, then

`A=(3)/(4)B` and will use that as a sub for A in the second equation:

`9B=8((3)/(4)B)+48` and

9B = 6B + 48 and

3B = 48 so

B = 16.

Now that we know B, we can use it to solve for A:

4A = 3(16) and

4A = 48 so

A = 12.

Then we can use that all the way back in the expression we set up for C:

C = A + 6 so

C = 12 + 6 so

C = 18

12 + 16 + 18 is the length of the string: 46cm