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Katyanochek1 [597]
3 years ago
8

Ben has 3.40 consisting of quaters and dimes. How many coins of each kind does he have if he has 22 coins?

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
4 0

Answer:

8 quarters and 14 dimes

Step-by-step explanation:

This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.  

• d+q=22 is an equation representing the total number of coins

• 0.10d+0.25q=3.40 is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get d=22-q. We now substitute this for d in the second equation.

0.10(22-q)+0.25q=3.40\\2.2-0.10q+0.25q=3.40\\2.2+0.15q=3.40

After simplifying, we subtract 2.2 across and divide by the coefficient of q.

2.2+0.15q=3.40\\0.15q=1.20\\q=8

We now know of the 22 coins that 8 are quarters. To find the number of dimes, we subtract 8 from 22 to get 14 dimes.


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Nimfa-mama [501]

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The population that gives the maximum sustainable yield is 45000 swordfishes.

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Step-by-step explanation:

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First Derivative Test

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-0.02\cdot p + 9 = 0

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Second Derivative Test

f''(p) = -0.02

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

f(450) = -0.01\cdot (450)^{2}+9\cdot (450)

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The maximum sustainable yield is 202500 swordfishes.

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