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torisob [31]
3 years ago
7

Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has

24 teeth, and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again?
Mathematics
1 answer:
Aleksandr [31]3 years ago
8 0

Answer:

5

Step-by-step explanation:

for the first gear

revolutions/teeth

1 / 24

2 / 48

3 / 72

4 / 96

5 / 120

6 / 144

for the second gear

revolutions/teeth

1 / 40

2 / 80

3 / 120

4 / 160

<em>the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.</em>

the way to get that amount of teeth is

24 = 2 \times 2 \times 2 \times 3 =  {2}^{3}  \times 3

40 = 2 \times 2 \times 2 \times 5 =   {2}^{3}  \times 5

the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.

{2}^{3} \times 5 \times 3 = 120

120 teeth are 5 revolutions for gear1 and 3 por gear2

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Answer:

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Step-by-step explanation:

2x + y = 20                                                                                     (1)

2x + 3y = 36                                                                                  (2)

(2) - (1) ⇔ (2x - 3y) - (2x + y) = 36 - 20

          ⇔ 2y = 16

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From (3) and (1), we have:

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⇔ 2x = 12

⇔ x = 6

So: C = x + y = 6 + 8 = 14

Conclusion : C = 14

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