Journal Instructions Complete the following Cookie Jar Problem concretely. You m
ID: 3197921 • Letter: J
Question
Journal Instructions Complete the following Cookie Jar Problem concretely. You may work forward or backwards. You must show each step and explain what you are doing visually. You can attach a word document if needed Do not work the problem symbolically by multiplying or dividing the fractions. There was a cookie jar on the table. Amanda who was hungry came and took two-fifths of the cookies in the jar. Then Beth came along and took one fourth of the cookies. Then Christine came along and ate one-third of the cookies in the jar. Then Danielle came and ate 3 cookies. Eleanor looked in the jar and saw 12 cookies left. How many cookies were in the jar to begin with?Explanation / Answer
Let x be the number of cookies in the beginning.
Number of cookies taken by Amanda = 2/5 * x = 2x/5.
=> The number of cookies remaining after taken by Amanda = x - 2x/5 = 3x / 5.
Number of cookies taken by Beth = 1/4 * 3x / 5 = 3x / 20.
=> The number of cookies remaining after taken by Beth = 3x / 5 - 3x / 20 = (12x - 3x) / 20 = 9x/20.
Number of cookies taken by Christine = 1/3 * 9x/20 = 3x/20.
=> The number of cookies remaining after taken by Christine = 9x/20 - 3x/20 = 6x / 20 = 3x/10.
Number of cookies taken by Danielle = 3
=> Number of cookies remaining after eaten by Danielle = 3x / 10 - 3.
Number of cookies left as seen by Eleanor = 12.
=> 3x/10 - 3 = 12
=> 3x/10 = 12 + 3
=> 3x/10 = 15
=> 3x = 15*10
=> x = 150/3
=> x = 50.
Therefore, there were 50 cookies in the jat to begin with.
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