## maximum possible number of chocolate bars per hour- DS quest

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### maximum possible number of chocolate bars per hour- DS quest

by guerrero » Fri Nov 23, 2012 6:12 am
What is the maximum possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour.

(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

Can any one help me interpret the wording into an equation please ? I am struggling

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by [email protected] » Sun Nov 25, 2012 11:43 pm
Let's define r as the maximum rate.

Our starting point is half the maximum rate, or r/2.

The increase in the rate is 300 chocolate bars per hour: r/2 + 300.

The end result is that the rate has increased by 25%. Remember, though, that our starting rate is r/2, so our new rate should be 25% greater than that.

r/2 + 300 = 1.25(r/2)
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by pemdas » Mon Feb 18, 2013 6:41 pm
guerrero wrote:What is the maximum possible number of chocolate bars per hour produced by a machine?

(1) Currently, the machine produces 1,200 chocolate bars per hour.

(2) If the chocolate bar production rate is increased from half the machine's maximum rate by 300 chocolate bars per hour, the rate is increased by 25%.

Can any one help me interpret the wording into an equation please ? I am struggling
we define chocolate bar (b) production function as b(h) where h is hour
st(1) b(h)=1200h implies that our maximum rate is db/dh=b(h)=1200. Assumptions: in case of production function being linear the above is true, otherwise Insuff
st(2) chocolate bar production rate is denoted as r and we have b(h)=rh. Increase from half the machine's max.rate implies b(h)=r and (r/2 + 300)=1.25 * r/2.
300=.25*r/2 and r=2400 Suff