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Prove that the two ratios below are equivalent. 9 cents for every 4 people and 18 cents for every 8 people.​

Respuesta :

Aisin

Answer:

R

Step-by-step explanation:

Let's rewrite this to the ratio of the amount of cents to the amount of people.

9 cents every 4 people ->  9:4
18 cents for every 8 people ->  18:8

Using the direct proportion : If one quantity increase/decrease an amount, the other one increase/decrease the same amount respectively.


So, we can rewrite 9:4 as 9x2/4x2 (both increase by 2 times) = 18:8

And since 18:8=18:8, these 2 ratios are equivalent.

Hi! Let me help you! :)

  • A ratio looks like so:
  • a:b (the ratio of a to b)
  • In this case, we have the following ratios:
  • 9:4 (also written as [tex]\displaystyle\frac{9}{4}[/tex]
  • 18:8 (also written as [tex]\displaystyle\frac{18}{8}[/tex]
  • Now, equivalent means equal, so we need to prove that these ration are equal to each other.
  • 9:4 and 18:8
  • To prove that the given ratios are equal, let's simplify the second ratio and write it in its simplest form.
  • To simplify it, divide the numerator and the denominator by 2:
  • 9:4
  • 9:4 and 9:4 are equal.
  • Thus, 9:4 IS equal to 18:8
  • Thus, the two ratios are equivalent.

Hope it helps!

~Stargazing~

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