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| Math Central | Quandaries & Queries |
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Question from keelan, a student: a number is divided by 5. then 3 is added to the quotient. after subtracting 10, the results is 30.what is the number. |
Hi Keelan,
I am going to describe the process in your problem using a table.
| Start | ||
| Divide by 5 | Step 1 | |
| Add 3 | Step 2 | |
| Subtract 10 | 30 | Step 3 |
The procedure is that you put a number in the start location, the green cell. In step 1 you divide by 5 and put the result in the Step 1 box. Next you add 3 and put the number in the Step 2 box. Finally you add 10 and the result in the Step 3 box is 30.
The challenge is that you don't know what number to start with but you can find it by working backwards. To arrive at 30 in the Step 3 box you subtracted 10 from the number in the Step 2 box above it. What number was in the Step 2 box? To arrive at this number in the Step 2 box you added 3 to the number in the Step 1 box. What number was in the Step 1 box? To arrive at this number in the Step 1 box you divided the number in the Start box by 5. What number was in the Start box?
Now that you know the number to put in the Start box, go forward through the process to make sure you end with 30.
Penny
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