8. Answers to Double Lines

Answer to Double Line Problem #1:

There are 20 girls in the class, and the ratio of Girls to Boys is 4:3.  How many Boys?
Draw the two parallel lines & label one "Girls"and other "Boys".

We are solving for Boys, so start with Girls.  Since there are "4" Girls per whatever and a total of 20 Girls, draw a series of vertical lines and label each one with increments of 4 (on the Girls line) until you get to 20.

Next: Since for every 4 Girls there are 3 Boys, we are going to use increments of 3 on the Boys line. Under the Girls "4", write a "3" on the Boys line, then a "6" under the Girls "8", then "9", "12", and finally "15" under the Girls "20".  Your Line Diagram should look like this:

There answer is 15.


Answer to Double Line Problem #2:
For every handful of popcorn I grab to eat, I drop 2 kernels to the floor.  Every handful of popcorn has eight kernels in it. The bowl of popcorn gave me 9 handfuls.  How many kernels landed on the floor?  

This one is a little tough so bear with me.  Here's what we know:

• 2 kernels dropped per handful.
• 8 kernels per handful
• 9 handfuls total.

We need to find:  Quantity of kernels on the floor.

The "handful" makes it a little confusing, however, we are solving for the number of kernels on the floor, so we need to break everything down into kernels and forget the handful nonsense.

8 kernels per handful and 9 handfuls total means there are 72 kernels total (8 x 9 = 72).

The ratio is 2 kernels to 8 kernels (per handful), or 2:8.

Draw up the double lines and use the labels "Dropped" and "Handful".  Start labeling the "Handful" line with increments of 8 until you get to the total of 72.  I grabbed 9 handfuls of 8, so there are 9 vertical lines (not including the zero line).

On the "Dropped" line, label the vertical lines with increments of 2 starting from zero.

The answer is 18 kernels on the floor for the dog to eat.