Question 1200411: I subtrated 8 from a certain number. I then multiply the result by3. The final ananswer is 21.find the original number Found 3 solutions by josgarithmetic, math_tutor2020, greenestamps:Answer by josgarithmetic(39620) (Show Source):
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x = starting unknown number
x-8 = subtract off 8
3(x-8) = multiply the result by 3
3(x-8) = 21 is the equation to set up
Let's isolate x.
To do so, we follow PEMDAS in reverse to undo what happens to x.
The last thing that happened was "multiply by 3", which means we undo that by dividing both sides by 3
3(x-8) = 21
3(x-8)/3 = 21/3
x-8 = 7
Then we add 8 to both sides to undo the "minus 8" aka "subtract 8".
x-8 = 7
x-8+8 = 7+8
x = 15
Here are all of the steps in one big block
3(x-8) = 21
3(x-8)/3 = 21/3
x-8 = 7
x-8+8 = 7+8
x = 15
Here is another route we could take through the use of the distributive property
3(x-8) = 21
3x-24 = 21
3x-24+24 = 21+24
3x = 45
3x/3 = 45/3
x = 15
Check:
Starting number = 15
Subtract off 8 to get 15-8 = 7
Triple the result: 7*3 = 21
The answer is confirmed.
The problem tells you what operations were performed on the starting number, and it tells you what number you ended up with.
One way to find what number you started with is to work backwards: take the number you started with and perform the OPPOSITE operations in the OPPOSITE order.
The operations you performed on the number you started with were (1) subtract 8 and (2) multiply by 3.
To get back to the original number from the number you ended up with, you need to (1) divide by 3 and (2) add 8.
21/3 = 7; 7+8 = 15
ANSWER: 15
Note that in solving the problem using the standard algebraic method those are exactly the steps you need to do -- divide by 3 and then add 8:
3(x-8) = 21 [given]
x-8 = 21/3 = 7 [divide by 3]
x = 7+8 = 15 [add 8]
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