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| Image source: hebbarskitchen.com |
Question:
My grandma uses a household bowl to measure ingredients for most of her dishes. While making khichdi, she usually puts one full dish and its eighth of dal into an empty pot, which brings it to the 500 ml mark. I need to find the measurement of the bowl so that I can figure out her reference point for future recipes. What is the bowl's measurement in millilitres?
Solution:
x + x⁄8 = 500
Try x = 80:
80 + 80⁄8 = 90
90 multiplied by what gives 500?
90 1
180 2
360 4
720 8
45 1⁄2
15 1⁄6
5 1⁄18
360 + 90 + 45 + 5 = 500 so we have 4 + 1 + 1⁄2 + 1⁄18 = 50⁄9 multiplied by 90 gives 500.
Thus x = 80 x 5 5⁄9
80 1
160 2
320 4
40 1⁄2
20 1⁄4
10 1⁄8
x = 80 + 320 + (80 + 320)/9
x = 400 + 400/9
9 1
18 2
36 4
72 8
144 16
288 32
576 64
x = 400 + 32 + 8 + 4 + 4/9 = 444 4⁄9 ml
Wow, beautiful and impressive! Not only did you write a meaningful and interesting false position word problem, you solved it with Ancient Egyptian multiplication and unit fractions! Bravo! Beautifully done.
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