A caterer has prepared 16 trays of hot food for an event. The trays are placed in warming boxes for delivery. Each box can hold 5 trays of food.

a. How many warming boxes are necessary for delivery if the caterer wants to use as few boxes as possible? Explain how you know.

b. If the caterer fills a box completely before filling the next box, what fraction of the last box will be empty?

a. 4 boxes are necessary to make the delivery.

b. The fraction empty of the last box will be 4/5

Step-by-step explanation:

The caterer has 16 trays and each box can hold 5 trays.

a. So, to know how many warming boxes we need we have to divide the total amount of trays by the amount the box can hold.

Quantity of boxes = 16/5=3.2

3 boxes wont hold all the trays, so we will need 4 boxes

b. Each box can hold 5 trays,

The first 3 boxes will hold 15 trays. So last box will hold 1 tray, in fraction is 1/5

1/5 of the last box is occupated

The empty space is 1 - 1/5=

The fractions have unlike denominators. First, we find the Least Common Denominator and rewrite the fractions with the common denominator.

1 - 1/5 = 5/5 - 1/5 = 5-1/5=4/5

The fraction empty of the last box will be 4/5

Answer: So, you have 16 trays of hot food, and each box can have a maximum of 5 trays.

a) if each box can have 5 trays then:

1 box can delivery 5 trays, that is not enough.

2 boxes can delivery 10 trays, that is not enough

3 boxes can delivery 15 trays, almost, but not enough

4 boxes can delivery 20 trays, this is it!

You also can see it in the next way: 16 trays/5 trays per box = 3.2 boxes.

But you can't use a 0.2 of a box, so here we need to round upwards!

3.2 rounded upwards is 4.

b) If you have 4 boxes, then you have 20 spaces for trays.

if each box is filled, you will put the first 15 trays in 3 boxes and fill them, and one leftover tray will go in the fourth box.

so this last box has one of five trays, this means that has 4 slots empty.

then the empty fraction is the empty slots divided by the total number of slots, this is: 4/5.