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svlad2 [7]
3 years ago
14

The ratio of runners to swimmers was 3:2. When 28 runners dropped out of the competition, the ratio became 5:6. How many total s

wimmers are competing?
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
7 0

The total of 42 swimmers are competing

Step-by-step explanation:

The given is:

  • The ratio of runners to swimmers was 3 : 2
  • When 28 runners dropped out of the competition, the ratio became 5 : 6

We need to find how many total swimmers are competing

∵ The ratio of runners to swimmers was 3 : 2

- Multiply each term of the ratio by x

∴ There are 3x runners and 2x swimmers

∵ 28 runners dropped out of the competition

∴ The number of runners who complete = 3x - 28

∵ The ratio became 5 : 6

- Equate the ratio between the new number of runners and the

   number of swimmers by 5 : 6

∵ The new number of runners = 3x - 28

∵ The number of swimmers = 2x

∴ \frac{3x-28}{2x}=\frac{5}{6}

- By using cross multiplication

∴ 6(3x - 28) = 5(2x)

- Simplify both sides

∴ 18x - 168 = 10x

- Add 168 to both sides

∴ 18x = 10x + 168

- Subtract 10x from both sides

∴ 8x = 168

- Divide both sides by 8

∴ x = 21

∵ The number of swimmers is 2x

∵ x = 21

∴ The number of swimmers = 2(21) = 42

The total of 42 swimmers are competing

Learn more:

You can learn more about the ratio in brainly.com/question/2707032

#LearnwithBrainly

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\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

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Step-by-step explanation:

Given the system of the equations

x+3y=5;\:x=-6y+14

solving by elimination method

\begin{bmatrix}x+3y=5\\ x=-6y+14\end{bmatrix}

\mathrm{Arrange\:equation\:variables\:for\:elimination}

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\begin{bmatrix}x+3y=5\\ 3y=9\end{bmatrix}

solve 3y=9 for y:

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