# Josie added a number to 11. she then multiplied the sum by 3 and divided the product by 9. if the quotient was 6, what was the number?

1
by Alonzozen407

2014-12-24T12:07:41+08:00

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In this kind of problem, we just make a linear equation and we will be able to find the answer. We use the art of transposing.
Let the unknown number be x:

[(x added to 11)multiplied by 3] divided by 9, and then the quotient is 6.
When translating it to symbols, it becomes like this:

[ ( x + 11 ) x 3 ] / 9   =   6
(multiply 9 to both sides to eliminate the "/9."

[ ( x + 11 ) x 3 ] 9/9 = 6 x 9
[ (x + 11 ) x 3 ] 1 = 54 or simply [ ( x + 11) x 3 ] =  54
( Use the distributive property of multiplication thingy)
( x + 11 ) x 3 or ( x + 11 ) 3 or 3 ( x + 11 )
3 ( x + 11 ) is the same as 3(x) + 3 (11)
3x + 33 =  54
3(transpose)
3x = 54 - 33
3x =  21
(Divide all sides by 3)
x = 7
Check: