We are given that Jenny finished 12 of 20 piano lessons from her book and that Liam finished the same percentage from his book of 30 lessons. We are asked to find the number of lessons Liam finished.
We can set up a proportion. We set the ratio of Jenny's finished lessons to her total lessons equal to the ratio of Liam's finished lessons to his total lessons, letting x represent the number of his finished lessons. Thus 12/20=x/30.
We can simplify 12/20 by dividing out the greatest common factor of the numerator and denominator. `(4(3))/(4(5))=3/5`
Now we have `3/5=x/30` . The common approach is to use the property of proportions that `a/b=c/d ==> ad=bc` (typically called cross-multiplying.) So 3(30)=5x ==> 90=5x. Dividing both sides by 5 we get x=18. Checking we see that `18/30=(6(3))/(6(5))=3/5=12/20`
Liam has finished 18 of his 30 lessons.
Once we have the proportion set up:`3/5=x/30` we note that 5(6)=30, so we can multiply 3/5 by 6/6 (a fancy form of one) to get 18/30 giving the answer of 18.
The problem mentions percent. Percent literally means out of 100, so we can convert 12/20 to a percent: 12/20=3/5=60/100 or 60%.
Now we can take 60% of 30: 30*60/100=1800/100=18, the number of completed lessons.