Julianne worked for three straight hours grading tests.

sanjib wrote:Julianne worked for three straight hours grading tests. If she graded 12 tests in the third hour, which was twice as many as she graded in the second hour, and three times as many tests as she graded in the first hour, how many tests did she grade in total?

From this explanation we can say
H3:H2:H1= 3:2:1 (where H3,H2.H1 means third hour second hour and 1st hour)

so H3= 3x/3+2+1= 3x/6(where x is total work)
=> 3x/6=12
=> x=24

which should be the answer.
Am I missing something?

if I am wrong then what should be the ratio please explain

The problem is with your ratio.

She graded twice as many in the third hour as in the second hour. You've written this as 3:2, when in fact it's 2:1.

Here are the actual ratios:

3rd:2nd = 2:1
3rd:1st = 3:1

Let's use "6" for the 3rd hour, since it's the LCM of 2 and 3, to get an overall ratio of:

6:3:2

So, we have 11 parts in total with a multiplier of 2 (6*2=12 tests that she actually graded in the 3rd hour). Therefore, she graded 11*2 = 22 tests.

Of course, it would have been MUCH quicker to just answer the question using common sense and grade 5 arithmetic instead of setting up ratios.

She graded 12 tests in the 3rd hour.

She graded half as many in the 2nd hour. Half of 12 is 6.

She graded 1/3 as many in the 1st hour. One third of 12 is 4.

12 + 6 + 4 = 22 tests in total.