Question 1210694: Good day! Please help me with this equation, I have been stuck on this problem for a long time:
I have a number in mind. I divided my number by 2 and then added 6. I doubled the result and subtracted one-fourth of what I have. Then I divided by 9. I was left with 5. What number did I have?
Found 4 solutions by math_tutor2020, josgarithmetic, ikleyn, MathTherapy:
Answer by math_tutor2020(3847)   (Show Source):
You can put this solution on YOUR website!
x = starting number
x/2 = 0.5x = taking half of that number
0.5x+6 = add on six
x+12 = double the previous expression
x+12 - 0.25(x+12) = 0.75(x+12) .... subtract off one quarter, aka 0.25 of the previous amount. Note you're left with three quarters, aka 0.75, of that amount.
0.75(x+12)/9 = 5 or 3(x+12)/36 = 5 since 0.75 = 3/4
Let's solve for x.
3(x+12)/36 = 5
3x+36 = 36*5
3x+36 = 180
3x = 180-36
3x = 144
x = 144/3
x = 48 is the starting number
Check:
x = 48
48/2 = 24 ... halving
24+6 = 30 ... adding on six
30*2 = 60 ... doubling
60 - 0.25*60 = 0.75*60 = 45 ... take away a quarter
45/9 = 5 .... dividing by nine
The answer is confirmed.
Answer by josgarithmetic(39840) (Show Source):
Answer by ikleyn(54016)  (Show Source):
You can put this solution on YOUR website! .
Good day! Please help me with this equation, I have been stuck on this problem for a long time:
I have a number in mind. I divided my number by 2 and then added 6.
I doubled the result and subtracted one-fourth of what I have.
Then I divided by 9. I was left with 5. What number did I have?
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It can be solved MENTALLY as a simple arithmetic problem, without using any equation/equations,
if you apply a backward method.
To do it, interpret the problem as simple elementary operations and write them step by step.
1. First, you divided a number by 2.
2. Then you added 6.
3. Then you doubled the result.
4. Then you subtracted one-fourth of that.
5. Then you divided by 9 and got 5.
Now let's make the opposite operations in the reverse order.
5. Before you divided by 9, you had 5*9 = 45.
4. Thus, 45 is 3/4 of what you had before step 4.
It is the same as saying that before step 4 you had  = 4*15 = 60.
3. So, before you doubled in step 3, you had 60/2 = 30.
2. Hence, before you added 6 in step 2, you had 30-6 = 24.
1. It means that your original number, before you divided the number by 2, was 2*24 = 48.
Doing it this way, you obtain/restore your original number as  .
It is the  , completing the solution.
I did not use any equation and solved everything to the end MENTALLY.
This problem, this method, and this solution are accessible for 4th-grade or 5th-grade students.
The backward method is a brilliant tool to develop young students' minds.
It strikes like lightning and turns the child's brain upside down,
revealing the nature of the solution in a completely new light.
Answer by MathTherapy(10863)  (Show Source):
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