# IT'S WEDDING SEASON!

Date of the Problem
July 08, 2024

In preparation for Tracy’s wedding, Lisa decides to throw Tracy a bridal shower. Lisa is planning to make the invitations herself. Each invitation requires 6 inches of ribbon to make a tiny bow on the front. If Lisa needs enough ribbon for 28 invitations, but must buy the ribbon by the half-yard, how many yards of ribbon must Lisa buy? Express your answer as a decimal to the nearest tenth.

If 28 invitations are needed and each one requires 6 inches (or half a foot) of ribbon, the invitations will require 28 × 0.5 = 14 feet of ribbon. This length is equivalent to 14 ÷ 3 = 4.667 yards. Since Lisa must buy the ribbon by the half-yard, she is forced to purchase 5 yards of ribbon for the invitations.

One of the most difficult tasks before a wedding for many couples is to do the seating chart for the reception. Tracy’s reception site has tables that seat 8 people or tables that seat 10 people.  If Tracy uses the tables that seat 8 people, she will have exactly 2 guests left over.  If Tracy uses the tables that seat 10 people, she will have exactly 4 guests left over. Tracy has between 200 and 250 guests. How many guests does Tracy have?

Knowing that there are 4 people left over if the 10-person tables are used tells us that the number of guests ends with the digit 4. Therefore, we can divide 204, 214, 224, 234 and 244 by 8 and see which of these numbers leaves us with a remainder of 2. There must be 234 guests at the reception.

One of the final tasks of the wedding day is often to cut the wedding cake. Tracy chose a wedding cake design that is made up of many smaller cakes. Each of the smaller cakes is the shape of a right cylinder with a height of 5 inches and a diameter of 10 inches.  Each smaller cake will be cut into exactly 30 pieces.  How many cubic inches of cake are in each piece? Express your answer as a decimal to the nearest tenth.

The smaller cakes are each in the shape of a right cylinder, so we will use the volume formula V = πr2h. The cakes each have a radius of 5 inches (since the diameter is 10 inches) and a height of 5 inches, so the volume of each cake is π(5)2(5) = 392.7 cubic inches. Dividing this volume into 30 equal pieces yields 392.7 ÷ 30 = 13.1 cubic inches per piece of wedding cake.

Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.

Page 2 contains ONLY PROBLEMS. ♦

Math topic
CCSS (Common Core State Standard)
Difficulty