Ms. Kiyama is fed up with all the legos around her living room so she decides to do something about it. She starts by getting rid of 23 of them because they are cracked. She then takes what is left and splits them evenly between the living room, James’ room, and Christopher’s room. When grandma comes over and sees how they can’t complete their creations with the legos in each room, she doubles each set for Valentine’s Day, so that each room contains 78 legos. How many legos were there to start?

Answer: 140

Step-by-step explanation:

Begin by dividing 78 by 2 to go back to the original amount before the grandmother doubled them. Then multiply by 3 (each room). Finally, add the 23 that were thrown away at the beginning.

Initially, there were 140 legos. Each room had 39 legos before grandmother doubled them to 78, so multiplying 39 by the 3 rooms gives 117 legos, plus 23 removed cracked legos equals 140 original legos.

The student is trying to calculate the original number of legos Ms. Kiyama had before any were removed or added. We know that each room ended up with 78 legos, and this number was obtained after grandmother doubled the amount in each room. Therefore, before being doubled, there would have been 78 / 2 = 39 legos in each room. Since these legos were distributed equally among three rooms, we'll multiply 39 legos by 3 rooms to find the total number of legos before they were doubled, which is 39 * 3 = 117 legos.

However, we must not forget that Ms. Kiyama initially got rid of 23 cracked legos. To find the original number, we need to add those 23 legos back to our total. So we take the 117 legos and add the 23 that were removed, giving us 117 + 23 = 140 legos. Therefore, Ms. Kiyama started with 140 legos.

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