SOLUTION: A number is doubled, and then seven is added. When the result is divided by forty, the quotient is two and the remainder is thirty-three. Find the original number.

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Question 972462: A number is doubled, and then seven is added. When the result is divided by forty, the quotient is two and the remainder is thirty-three. Find the original number.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A number
That's N
is doubled,
That's 2N
and then seven is added.
That's 2N + 7
When the result is divided by forty,
That's %282N%2B7%29%2F40
the quotient is two and the remainder is thirty-three.
That says %282N%2B7%29%2F40%22%22=%22%222%2633%2F40

That's because you put the remainder over the divisor 
when you finish dividing. The divisor is 40 because that's
what we divided by.

We change the mixed number to an improper fraction 113%2F40

Now we have this equation:

%282N%2B7%29%2F40%22%22=%22%22113%2F40

We multiply both sides by 40, and get: 

2N + 7 = 113

We subtract 7 from both sides:

    2N = 106

We divide both sides by 2

    N = 53

-------

Now we check
A number
That's 53
is doubled,
That's 106
and then seven is added.
That's 106 + 7 = 113
When the result is divided by forty,
That's this division

     2
40)113
    80
    33
the quotient is two and the remainder is thirty-three.
It checks.

Edwin