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3 years ago

11

Mathematics

1 answer:

IrinaVladis [17]3 years ago

8 0

Answer:

D. Multiply the second equation by 3. The solution is x = 12, y = 10

Step-by-step explanation:

Given:

x + 3y = 42 (first equation)

2x - y = 14 (second equation)

To solve by elimination, starting with elimination of the y-variable, multiply the second equation by 3 to get a third equation.

2x - y = 14 (2nd eqn.) × 3

6x - 3y = 42 (3rd equation)

Add the 3rd equation and the 1st equation together.

x + 3y = 42 (first equation)

6x - 3y = 42 (3rd equation)

7x = 84

7x/7 = 84/7

x = 12

To find y, substitute x = 12 in the first equation

x + 3y = 42 (first equation)

12 + 3y = 42

12 + 3y - 12 = 42 - 12

3y = 30

3y/3 = 30/3

y = 10

Solution is x = 12, y = 10

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A tap can fill a bucket in 6 hours. After half the bucket is filled, three more similar taps are opened. What is the total time

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The total time taken to fill the bucket completely is 3 hours 45 minutes

The time taken to fill the bucket by one tap= 6 hours

Then the time take by one tap to fill half of the bucket= 3 hours

Part filled by one tap in one hour = $\frac{1}{6}$

Part filled by four taps in one hour = $4(\frac{1}{6})=\frac{4}{6}=\frac{2}{3}$

Given, that after half the bucket is filled, three more similar taps are opened

Then the remaining part = $1-\frac{1}{2}=\frac{1}{2}$

Time taken to fill the half of the bucket= $(\frac{1}{2} )(\frac{2}{3})=\frac{3}{4}$ hours

Convert the hours to minutes

$(\frac{3}{4})60=45$ minutes

Therefore,

Total time taken to fill the bucket= The time taken by one tap to fill half of the bucket+ Time taken by 4 taps to fill the half of the bucket

=3 hours+ 45 minutes

=3 hours 45 minutes

Hence, The total time taken to fill the bucket completely is 3 hours 45 minutes

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