a number machine takes any number put into it, multiplies it by 3 and then subtracts 2. reuben put a number into the machine. he took the new number that came out and put that number back into the machine. He took the new number that came out and put that back into the machine. the number that came out this time was 271. what number did reuben originally put into the machine?
Reiny already answered this question but I didn't get the explanation
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first number ----> machine ----> 2nd number ---> machine ---> 3rd number ----> machine ----> 4th number = 271
Machine basically multiplies the number by 3 and subtracts 2.
So we work backwards. 271 + 2 = 273. Divide it by 3 to get the 3rd number, 91.
Do the same thing 2 more times. 91 +2 = 93.
93/3 = 31. 31 + 2 = 33. 33/3 = 11. So the original number is 11. Check work
11 * 3 - 2 = 31. (2nd number) 31 * 3 - 2 = 91. (3rd number) 91 * 3 - 2 = 273 -2 = 271. TADA! we win :P
To solve this problem, let's break down the steps that Reuben followed:
1. Reuben puts a number into the machine.
2. The machine multiplies it by 3.
3. The machine subtracts 2 from the result.
4. Reuben takes the new number that came out and puts it back into the machine.
5. The machine multiplies it again by 3.
6. The machine subtracts 2 from the result.
7. Reuben takes the new number that came out and puts it back into the machine.
8. The machine multiplies it by 3.
9. The machine subtracts 2 from the result.
10. The final number that came out was 271.
Now, let's work backward step by step to find the original number Reuben put into the machine. We will reverse each of the operations that were done by the machine.
Step 10: The final number that came out was 271.
To backtrack, we need to add 2 since the machine subtracted 2. So, 271 + 2 = 273.
Step 9: The number before this was 273.
To reverse the "multiplied by 3" operation, we need to divide by 3. So, 273 ÷ 3 = 91.
Step 8: The number before this was 91.
Also, divide by 3 here: 91 ÷ 3 = 30.33 (rounded to 2 decimal places).
Step 7: The number before this was 30.33.
Again, divide by 3: 30.33 ÷ 3 = 10.11 (rounded to 2 decimal places).
Step 6: The number before this was 10.11.
Once more, divide by 3: 10.11 ÷ 3 ≈ 3.37 (rounded to 2 decimal places).
Step 5: The number before this was 3.37.
Now, add 2 to it since the machine subtracted 2: 3.37 + 2 = 5.37.
Step 4: The number before this was 5.37.
Divide by 3: 5.37 ÷ 3 ≈ 1.79 (rounded to 2 decimal places).
Step 3: The number before this was 1.79.
Again, add 2: 1.79 + 2 = 3.79.
Step 2: The number before this was 3.79.
Dividing by 3: 3.79 ÷ 3 = 1.26 (rounded to 2 decimal places).
Step 1: The number before this was 1.26.
Finally, we have reached the beginning. So, the original number that Reuben put into the machine was approximately 1.26.
Therefore, the original number that Reuben put into the machine was approximately 1.26.