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Nadusha1986 [10]
3 years ago
13

Determine the length of PN and the value of y

Mathematics
1 answer:
e-lub [12.9K]3 years ago
7 0

Answer:

Side PN=26

y=16

Step-by-step explanation:

I put a photo of my work. It’s easier to do that then to try and put it all in words

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Emily's piggy bank contains twice as many dimes as nickels. It contains two more quarters than nickels. Emily calculates that if
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Answer:

Emily has 10 nickels, 20 dimes and 12 quarters in her piggy bank

Step-by-step explanation:

The number of dimes in Emily's piggy bank = 2 × The number of nickels

The number of quarters in it = 2 + The number of nickels

Whereby;

The number of quarters = The number nickels

The number of dimes = The number of quarters

The number of nickels = The number of dimes

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Let 'x' represent the number of dimes, let 'y' represent the number nickels, and let 'z' represent the number quarters in Emily's piggy bank, we have;

x = 2 × y

z = 2 + y

The total amount in the piggy bank is therefore;

Total = C = x×0.1  + y×0.05 + z×0.25 = 2·y×0.1 + y × 0.05 + (2 + y) × 0.25 = 0.5·y + 0.5

C = 0.5·y + 0.5

With the second condition, we have;

z = y

x = z

y = x

We get

x × 0.1 + y × 0.05 + z × 0.25 = y ×0.1 + y×0.05 + y×0.25 = 0.4·y = C - 1.5

∴ C = 0.4·y + 1.5

Which gives;

0.5·y + 0.5 = 0.4·y + 1.5

0.1·y = 1.5 - 0.5 = 1

y = 1/0.1 = 10

y = 10

Therefore;

x = 2×y = 2 × 10 = 20

z = 2 + y = 2 + 10 = 12

Therefore;

The number number of nickels in her piggy bank, y = 10

The number of dimes in her piggy bank, x = 20

The number of quarters in her piggy bank, z = 12

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