lheiannie07 wrote:A machine at the golf ball factory can produce 16 golf balls in 5 minutes. If several of these machines work independently and each machine performs at the same rate, how many machines are needed to produce 32 golf balls per minute?

A) 3
B) 6
C) 8
D) 10
E) 13

Use the following equation:

(machines)(time) / output = (machines)(time) / output

In the equation above:
Machines and time are INVERSELY PROPORTIONAL.
As the number of machines increases, the amount of time required to produce the same output decreases.
Machines and output are DIRECTLY PROPORTIONAL.
As the number of machines increases, the amount of output also increases.
Time and output are also DIRECTLY PROPORTIONAL.
As the amount of time increases, the amount of output also increases.

In the problem above:
1 machine takes 5 minutes to produce 16 golf balls, and we are asked how many machines are needed to produce in 1 minute 32 golf balls.
Thus, we get the following equation:
(1 machine)(5 minutes)/(16 golf balls) = (x machines)(1 minute)/(32 golf balls)
5/16 = x/32
x = (5)(32/16) = 5*2 = 10.

The correct answer is D.

A machine at the golf ball factory can produce 16 golf balls in 5 minutes. If several of these machines work independently and each machine performs at the same rate, how many machines are needed to produce 32 golf balls per minute?

A) 3
B) 6
C) 8
D) 10
E) 13

Hi lheiannie07,
Let's take a look at your question.

The machine produces 16 golf balls in 5 minutes.
1 golf ball can be produced in (5/16) minutes.

32 golf balls can be produced in:
$$=\ \frac{5}{16}\times32$$
$$=\ 5\times2\ =\ 10\ $$

Therefore, one machine will produce 32 golf balls in 10 minutes.

But the question asks that if several of these machines work independently and each machine performs at the same rate, how many machines are needed to produce 32 golf balls per minute?
So if one machine is producing 32 golf balls in 10 minutes.
Then 10 machines will be needed to produce 32 golf balls per minute.
Therefore, Option D is correct.

Hope it makes sense.
I am available if you'd like any follow up.

I'd fall back on the trusty equation Work = Rate * Time.

Here, we know that each machine follows the equation

Work = Rate * Time
16 = Rate * 5

(since work = 16 golf balls and time = 5 minutes)

Dividing both sides by 5, we get Rate = 16/5, so each machine works at a rate of 16/5 of a golf ball per minute.

From here, our equation becomes

32 = (# of machines) * 16/5 * 1

(since work = 32 golf balls, each machine's rate = 16/5, and the time = 1 minute)

That's a cinch to solve, and we're done! The # of machines = 10.