Jane and Daphne each bought a certain number of ribbons from a shop. Jane gave 1/6 of her ribbons to Daphne. Then Daphne gave 2/5 of what she had back to her. Next, Jane counted all her ribbons and gave 1/4 of them to Daphne. In the end, Jane had 54 ribbons and Daphnehad 51 ribbons. How many ribbons did each of them buy from the shop at first?
Please help me with this qns and show me the steps to finding the ans?
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Reply:You have all the information you need. Think of it as doing a maze puzzle. Some people find it easier working backwards. This is how you solve this particular problem - work backwards. Let's look at the information we have:
Jane ended up with 54 ribbons. Daphne ended up with 51. That tells us they initially bought a total of 105 ribbons. That's our sanity check as we go through the problem.
Jane gave Daphne 1/4 of her ribbons, which left Jane with 54. If she gave away 1/4, that means she has 3/4 left, or 54. Now we figure out how many she had before giving away 1/4 by calculating what 54 is 3/4 or 75% of. To do that, you can either divide 54 by 0.75 or multiply 54 by the inverse of 3/4, which is 4/3. The total comes out to be 72. So Jane gave 1/4, or 18 ribbons, to Daphne. If Jane had 72, then Daphne had 33, for a total of 105.
Now, Daphne had 33 left after giving 2/5 to Jane, which means she had 3/5 left. Choose one of the methods above to figure out what 33 is 3/5, or 60% of. It turns out to be 55. Now we see that Daphne gave Jane 22 ribbons and had 33 left. If Daphne had 55, then Jane must have had 50, for a total of 105.
Jane had 50 after giving Daphne 1/6. Again, as before, we can figure out that Jane has 5/6 left. Jane initially gave Daphne 10 ribbons from her original purchase of 60 ribbons. If Jane bought 60 ribbons, Daphne must have bought 45, for a total of 105.
Hope this helps!
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