SOLUTION: Mary counted 15 cupcakes left from the whole batch that Mother made for the picnic. "We've already eaten two-fifths," she shouted. How many cupcakes did Mother bake. I tried 15* 2/

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Question 1086603: Mary counted 15 cupcakes left from the whole batch that Mother made for the picnic. "We've already eaten two-fifths," she shouted. How many cupcakes did Mother bake. I tried 15* 2/5 and came up with 6 eaten from the 15. I then added 6 to the 15 showing that 21 cupcakes were made. However, that seems to tell me that the two-fifths made be in error. I know that the unknown is the total amount of the cupcakes baked. Unclear as to how to find the unknown with a problem as 15 X 2/5=x or 15 + 2/5x=x. Thank you.

Answer by MathTherapy(10552) About Me  (Show Source):
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Mary counted 15 cupcakes left from the whole batch that Mother made for the picnic. "We've already eaten two-fifths," she shouted. How many cupcakes did Mother bake. I tried 15* 2/5 and came up with 6 eaten from the 15. I then added 6 to the 15 showing that 21 cupcakes were made. However, that seems to tell me that the two-fifths made be in error. I know that the unknown is the total amount of the cupcakes baked. Unclear as to how to find the unknown with a problem as 15 X 2/5=x or 15 + 2/5x=x. Thank you.
No, no, no! It can't be done like that!
Since 2%2F5 was eaten, 3%2F5 of the total made, was left
This means that 15 represents 3%2F5 of the total number made.
With N being the number baked, this leads to the following PROPORTION: %283%2F5%29%2F1++=+15%2FN
matrix%281%2C3%2C+%283%2F5%29N%2C+%22=%22%2C+15%29 ------- Cross-multiplying
Number baked, or highlight_green%28matrix%281%2C5%2C+N%2C+%22=%22%2C+5%2815%29%2F3%2C+or%2C+25%29%29