## A bottle manufacturing company has $$5$$ identical machines, each of which produces bottles at the same constant rate.

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### A bottle manufacturing company has $$5$$ identical machines, each of which produces bottles at the same constant rate.

by VJesus12 » Tue Sep 22, 2020 7:27 am

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A bottle manufacturing company has $$5$$ identical machines, each of which produces bottles at the same constant rate. How many bottles will all $$5$$ machines produce running simultaneously for $$x$$ hours?

(1) Running simultaneously, $$3$$ of the machines produce $$72,000$$ bottles in $$2x$$ hours?

(2) Running simultaneously, $$2$$ of the machines produce $$24,000$$ bottles in $$x$$ hours?

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### Re: A bottle manufacturing company has $$5$$ identical machines, each of which produces bottles at the same constant rat

by swerve » Tue Sep 22, 2020 12:08 pm

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## Global Stats

VJesus12 wrote:
Tue Sep 22, 2020 7:27 am
A bottle manufacturing company has $$5$$ identical machines, each of which produces bottles at the same constant rate. How many bottles will all $$5$$ machines produce running simultaneously for $$x$$ hours?

(1) Running simultaneously, $$3$$ of the machines produce $$72,000$$ bottles in $$2x$$ hours?

(2) Running simultaneously, $$2$$ of the machines produce $$24,000$$ bottles in $$x$$ hours?

Let the rate of each machine be r. Thus we have to find out the value of $$5\cdot r \cdot x$$. Thus, it is sufficient to find the value of $$r \cdot x$$.
Statement 1 states that $$3 \cdot r \cdot 2x= 72000$$. No need to calculate anything, as we know the value of $$r∗x$$. Sufficient $$\Large{\color{green}\checkmark}$$
Statement 2 states that $$2∗r∗x = 24000$$. Just as above, Sufficient $$\Large{\color{green}\checkmark}$$