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2 years ago

Five consecutive multiples of 3 yield a sum that is equal to the product of 7 and 15. What are these multiples?

Mathematics

1 answer:

Andrej [43]2 years ago

5 0

Answer:

15, 18, 21, 24, 27

Step-by-step explanation:

Five multiples of 3 means we have 5 terms we are adding together to = 105.

For the sake of having something to base each one of these terms on, let's say that the first term is 3. It's not, but 3 is a multiple of 3 and we have to start somewhere. These terms go up by the next number that is divisible by 3. After 3, the next number that is divisible by 3 is 6. The next one is 9, the next is 12, the last would be 15.

Let's then say that 3 is the first term, and we are going to say that is x.

To get from 3 to 6, we add 3. Therefore, the second term is x + 3.

To get from 3 to 9, we add 6. Therefore, the third term is x + 6.

To get from 3 to 12, we add 9. Therefore, the fourth term is x + 9.

To get from 3 to 15, the last term, we add 12. Therefore, the last term is x + 12.

The sum of these terms will then be set to equal 105:

x + (x + 3) + ( x + 6) + ( x + 9) + ( x + 12) = 105

We don't need the parenthesis to simplify so we add like terms to get

5x + 30 = 105. Subtract 30 from both sides to get

5x = 75 so

x = 15

That means that 15 is the first multiple of 3.

The next one is found by adding 3 to the first: so 18

The next one is found by adding 6 to the first: so 21

The next one is found by adding 9 to the first: so 24

The last one is found by adding 12 to the first: so 27

15 + 18 + 21 + 24 + 27 = 105

Notice that all the numbers are, in fact, consecutive multiples of 3 as the instructions stated.

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