Question

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

Answer 1

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
  `\displaystyle(9)/(4)`
• 18:8 (also written as
  `\displaystyle(18)/(8)`
• 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~

Answer 2

R

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.