Question

In a marching band there are 24 trombones and 15 snare drums. Heather says the ratio of trombones to snare drums is 24:15. Audrey disagrees and says the ratio is 8:5. Actually, Heather and Audrey are both correct. Explain why these are equivalent ratios. Question 1 options:

Answer 1

Step-by-step explanation:

We are told that in a marching band there are 24 trombones and 15 snare drums.

Heather says the ratio of trombones to snare drums is 24:15. We can represent Heather's ratio in a fraction as:
`(24)/(15)`

Audrey disagrees and says the ratio is 8:5. We can represent Audrey's ratio in a fraction as:
`(8)/(5)`

As proportions states that two quantities are equal, so we will use proportions to find whether both are right or not.

`(24)/(15)=(8)/(5)`

Upon reducing left side fraction of our equation to lowest terms we will get,

`(3*8)/(3*5)=(8)/(5)`

Upon cancelling out 3 we will get,

`(8)/(5)=(8)/(5)`

We can see that both sides of our equation are equivalent, therefore, Heather and Audrey are both correct.