Three sizes of popcorn buckets are on sale at a movie theatre. The large bucket holds 15 1/2 cups of popcorn. The medium bucket holds 1/3 of the amount of the large bucket. The small bucket holds 2/4 of the amount of the medium bucket. How many cups does the medium bucket hold?

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Step-by-step explanation:

The medium bucket can hold 5 and 1/6 cups of popcorn.

Step-by-step explanation:

Remember that for mixed numbers, like "4 and 1/5", the way of writing that number is (4 + 1/5).

Now, let's solve the question:

We know that the large bucket holds (15 + 1/2) cups.

We also know that the medium bucket holds 1/3 of the large bucket, and we want to know how many cups does the medium bucket hold.

This is just (1/3) times the amount that the large bucket holds, so we have:

(1/3)*(15 + 1/2) cups

Using the product distributivity, we can write:

(1/3)*(15 + 1/2) cups = ( (1/3)*15 + (1/3)*(1/2) ) cups = (5 + 1/6) cups

Then we can conclude that the medium bucket can hold 5 and 1/6 cups of popcorn.

1) The medium size bucket holds 31/6 or 5 1/6 cups of corn

2) The small size bucket holds 31/12 or 2 7/12  cups of corn.

Improper fractions:

In order to solve this problem, we need to work with improper fractions       (such fractions got this name because an improper fraction is always bigger than one.

An example of an improper fraction is: 11/8

11/8    ( notice that  11/8  is equal to 1,375 ) so we can express that type of fraction as 1 3/8, in order to get the original fraction we must multiply the denominator by the integer (8*1)  and add the numerator (3) copying the same denominator)

In our particular case:

We got that the large bucket holds 15 1/2 cups of corn

15 1/2   =  (15*2 + 1)/2   = (30 + 1 )/2 = 31/2

Then 31/2 cups are the volume of the large bucket.

The medium bucket is 1/3 of that quantity or

1/3 * 31/2  =  (1)*(31)/(3)*(2) = 31/6  

Then the medium-size bucket holds 31/6 or 5 1/6 cups of corn

and finally, the small bucket is 2/4  = 1/2  of the medium bucket

(1/2)*(31/6)  =  ( 1*31)/(2)(6) = 31/12

Then the small size bucket holds 31/12 or 2 7/12  cups of corn.

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.