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Brilliant_brown [7]
3 years ago
13

Two numbers are of the ratio 3:5. If their difference is 18, find the numbers.​

Mathematics
1 answer:
Sergio039 [100]3 years ago
4 0

x \div y = 3 \div 5  \\ it \: means  =  \\ 3y = 5x \\ x - y = 18 \\

To solve we multiply the last equation by 5 and we get the following:

5x-5y=90

But 5x=3y and we replace it in this equation:

3y-5y=90

-2y=90

y=-45

and x-(-45)=18 , x+45=18

x=-27

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(i) see first attached diagram

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Step-by-step explanation:

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<u />

<u>Part (i)</u>

see first attached diagram

<u>Part (ii)</u>

The angles marked in blue on the second attached diagram are Consecutive Interior Angles.  In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°        

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

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⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

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<u>Part (iii)</u>

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

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⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

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