division problem

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12

There are a few ways to tackle this question.

One way is to examine a few other fractions.
7/2 = 3 with remainder 1.
7/2 = 3 1/2 = 3.5
Notice that 0.5 = 1/2

Another example:
11/4 = 2 with remainder 3.
11/4 = 2 3/4 = 2.75
Notice that 0.75 = 3/4

Now onto the question....

So, we know that x/y = some value with remainder 9
If x/y = 96.12, we can conclude that 0.12 = 9/y
Now solve for y.
0.12 = 9/y
12/100 = 9/y [rewrite 0.12 as 12/100]
Simplify to get: 3/25 = 9/y
At this point, we might already see that y = 75. If we don't spot this, we can always cross-multiply.
We get: 3y = (25)(9)
Solve to get y = 75

Cheers,
Brent

ash_maverick wrote:When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A. 96
B. 75
C. 48
D. 25
E. 12
---please explain .

We can create quotient/remainder equation, where the quotient Q is an integer:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula, we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 and determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer. See below.

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

Answer: B