How many fireflies did Karen catch?

Question

Dahlia caught twice as many fireflies as Andrew. Kaitlyn caught 16 more fireflies than Andrew. All together, Dahlia, Kaitlyn, and Andrew caught a total of 88 fireflies. How many fireflies did Karen catch? 

 

A. Solve this problem in two ways, with a strip diagram and with an equation.

Answer 1

I will show you the equation method first because it makes more sense and is more efficient to understand.  To write the equation, we need to define variables for each person.  Notice that the amounts of fireflies caught by several people are being compared to a common person who caught a certain number of fireflies.  That person is Andrew.  He is our reference point.

 

Let the amount Andrew caught = x

Let the amount Dahlia caught = 2x

Let the amount Kaitlyn caught = x + 16

 

Together, they caught a total of 88 fireflies.  Using the variables and the total amount, we can write and equation to represent the total number of fireflies caught.

 

x + 2x + x + 16 = 88

 

Solve for x from this equation.  When you have solved for x, you will find out how many Andrew caught.  You will then substitute that value of x for Dahlia and Kaitlyn to find their amounts too.

 

 

Now here is the strip diagram that I believe common core standards wants you to do.  I find this method to be unnecessary and a bit confusing, but here it goes.

 

I will use a solid line to represent the total number of fireflies caught.  Then I will use 3 different sized dotted lines to represent the number each person caught with their endpoints aligned to each other, and I will label them.  Based on the problem description, Andrew will have the least number.

 

    |___________________________________________________________|   ----> total caught

 

    |------|   Andrew

 

             |--------------|   Dahlia

                                

                                 |------------------------------------------------------------|   Kaitlyn

 

 

 

The three different sized segment joined together is equivalent to the solid line.  Do you remember adding joining line segments to find the distance of a major line in previous classes?