10. Answers to Tape Diagrams

Answer to Tape Q1:

The ratio of pepperoni to sausage is 3 to 1.  We used up 24 slices of pepperoni.  How many pieces of sausage did we use?

We can see from the problem that the ratio is 3:1.  So we need three boxes and one box.  We also know the total Pepperoni is 24.  So set up the Tape diagram with what we know: 

Next:  figure the magic number (remember:  all of the numbers inside the boxes must be the same). What goes into 24 equally three times?…why the number 8 of course.  Write the number 8 in all of the boxes.   

Now calculate the quantity of sausage used (Hmmm, let’s see…. 1 times 8 = 8!!!).

Answer to Tape Q2:   It’s Pizza Day at the cafeteria Can’t get enough of that Pizza).  There are two cafeteria lines - Sixth graders in one line and Fifth graders in the other.  There are two Sixth graders for every three Fifth graders.  You count 40 Sixth graders in your line.  How any Fifth graders are in line?

Set up the Diagram with what we know:  

•  A ratio of 2:3 (sixth graders to fifth graders).  Hence show two boxes and three boxes.  Label the three-box row "fifth graders" and the two-box row "sixth graders”.
• We also know the number 40 for the total sixth graders - so 40 on the sixth grade line.  Your diagram should now look like this: 

Next:  Find the magic number:  Two sixth graders boxes add up to 40.  The magic number must be 20 (40 divided by 2).   Now write 20 in all of the boxes.

Add up the number of “20s"in the fifth grade boxes and write the total in the fifth grade line on top (which should be 60).   Voila. 

Answer to Tape Q3:  You have major math homework tonight - 30 math problems…YIKES!.  You are also starving for those homemade Chocolate Chip cookies.  Mom says you can have two cookies for every 6 math problems you work out correctly.  You finish all of the math homework correct.  How many cookies do you get?

What do we know?

• The Ratio is 2 cookies to 6 Math, or 2:6.  (hence two boxes and six boxes)
• The bonus number is the total Math problems at 30.

Set up the diagram: 

Now solve for the magic number.  Six equal boxes adding up to 30.  (30 divided by 6 = 5).  Write “5" in all of the boxes.

  The quantity of cookies is 10.