We are told that every 9th person gets free popcorn and every 6th person gets free apple juice at the movie theater. We want to show if the 36th person is the first to get both free popcorn and apple juice.
Since every 9th gets free popcorn, then the 9th and 18th and 27th and 36th people get it. We can use numbers and show this as multiples of 9.
9, 18, 27, 36, 45, 54, ...
And we repeat it for every 6th and the free juice.
6, 12, 18, 24, 30, 36,....
Shani thinks 36 comes first, and she's wrong. 18 appears on the list before 36 as something that's common. What are we finding is the lowest common muliple of 6 and 9.
6 = 2 x 3
9 = 3 x 3
The lowest common multiple will have a 2, a 3, and a second 3 (because we don't double count). 2 x 3 x 3 = 18. This matches up to the list of multiples.
Thus, Shani is wrong that the 36th person gets both free items, as she did not account for the 18th person gettting both free items
If you have to unknown variables, you have to eliminate one, e.g. Like this:
2×(2y-10)+3y=1240. Now there is only one unknown variable
4y-20+3y=1240
7y-20=1240
7y=1260
y=1260/7=180
Now you can calculate x
x=2y-10=2×180-10=360-10=350. ( You can also use the other equation but This one is easier)
Answer:
49 third graders
Step-by-step explanation:
From the question:
The music teacher receives 9 boxes of recorders and there are six recorders in each box
The total number of recorders the teacher received =
1 box = 6 recorders
9 boxes = x
Cross Multiply
x = 9 × 6 recorders
x = 54 recorders.
She hands them out to third graders and has 5recorders left .
How many third graders received a recorder?
The amount of recorders shared =
54 recorders - 5 recorders
= 49 recorders
If 1 recorders was given to a third grader,
Therefore, the amount of third graders that received a recorder is 49 third graders
Step-by-step explanation:
as any other fully symmetric 3D object, the volume is
base area × height.
the area of a circle is
pi×r²
so, we have in our case
pi×13²×9 = 3.14×169×9 = 4,775.94 cm³
Answer:
0.75
Step-by-step explanation:
9/12 equals 3/4 which is 0.75
