Quandaries and Queries

I have a problem solving project that has to be worked out backwards. Can you help me?

Triva went to the ardcade at the state fair to win some goldfish. She already had some goldfish at home, but wanted more. She won enough goldfish to double her stock. Her mom made her give four away. She put her new ones in the tank with the others, by the morning half of the goldfish had died. Triva's friend gave her six more. The next morning two-thirds of her goldfish died. She was left with two goldfish after giving one to a friend. How many goldfish did she start with?

I have been working on the problem but cant seem to get the answer right,
Thank You
Melody

Hi Melody,

I would construct a table with two columns, and a row for each event that happened. The two columns are "the number of fish before the event" and "the event". Here is my table.

 Number of fish before The action Triva doubled her stock she gave four away one-half died a friend gave her six two-thirds died she gave one to a friend the final number

Now start filling in the ble from the bottom up. The final number is 2 and hence, before she gave one to a friend, she had 3.

 Number of fish before The action Triva doubled her stock she gave four away one-half died a friend gave her six two-thirds died 3 she gave one to a friend 2 the final number

Before that, two-thirds of her fish died. Hence the 3 fish she has now is one-third of the fish she had before that. Hence she had 9 fish before two-thirds died.

 Number of fish before The action Triva doubled her stock she gave four away one-half died a friend gave her six 9 two-thirds died 3 she gave one to a friend 2 the final number

Complete the table and then check your answer by going forward.

Penny

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