Grades 3-4 Video Solutions 2020-2020Levels34prob14

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Problem number 14. The sum of three numbers is 50. Karen subtracts a secret number from each of these three numbers. She gets 24, 13, and 7 as the result. Which of the following  is one of the original three numbers? A, 9, B, 11, C, 13, D, 17, E, 23. We know the result  that Karen gets when she subtracts the secret number. We also know the sum of the three numbers before Karen subtracted anything. She started with three numbers, and she subtracted  the secret number from each one. That means that she subtracted the secret number three times. The sum of the original three numbers was 50, and the sum of the three numbers after  subtracting is 24 plus 13 plus 7, which is, 13 plus 7 is 20, plus 24 more is 44. So in total, Karen subtracted 6, because 50 minus 6 is 44. Since she subtracted the secret number  from three different numbers, that means that 3 times the secret number is 6, and the secret number is 2. She subtracted 2 from one number, 2 from another, and 2 from another.  That means that the original numbers were 24 plus 2, which is 26, 13 plus 2, which is 15, and 7 plus 2, which is 9. We can check that that indeed makes 50. 6 plus 5 is 11,  plus 9 more is 20. 2 plus 2 is 4, plus 1 more is 50. So here are the original numbers. Now  the problem is asking which of the answers is among the original numbers. We see that 9 is,  and that should be the only one. 11 is not one of the original numbers. 13 is not one of the numbers. It is one of the numbers she got as a result after subtracting a secret number,  but it's not one of the original numbers. 17 is not one of the original numbers, and 23 also is not one of the original numbers. The answer is A, 9.

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