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butalik [34]
2 years ago
6

The sum of two numbers is 30. If three times the smaller number is equal to two times the bigger one, find the numbers. ​

Mathematics
1 answer:
MAVERICK [17]2 years ago
4 0
  • Let the smaller number be x and the bigger number be y.
  • Therefore, 3x = 2y =  > x =  \frac{2y}{3}x + y = 30 \\  =  >  \frac{2y}{3}  + y = 30 \\  =  >  \frac{2y + 3y}{3}  = 30 \\  =  >  \frac{5y}{3}  = 30 \\  =  > y =  \frac{30 \times 3}{5}  \\  =  > y = 18
  • Therefore, the smaller number = 30 - 18 = 12

<u>Answers:</u>

<u>Answers:The smaller number is 12.</u>

<u>Answers:The smaller number is 12.The bigger number is 18.</u>

Hope you could understand.

If you have any query, feel free to ask

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Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have x^{2} -10x and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square: x^{2} -10x+25=(x-5) ^{2}

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have 2( x-5) ^{2}-53 and when we multiply that out it does not give us what we started with. It gives us 2 x^{2} -20x+50-53=2 x^{2} -20x-3

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We do this as follows: 2(x-5) ^{2}-53-50 which gives us the final expression we seek:

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If you multiply this out you will get the exact expression we were given. This means that:
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