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: $\frac{24}{15}$

Audrey disagrees and says the ratio is 8:5. We can represent Audrey's ratio in a fraction as: $\frac{8}{5}$

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

$\frac{24}{15}=\frac{8}{5}$  

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

$\frac{3*8}{3*5}=\frac{8}{5}$  

Upon cancelling out 3 we will get,  

$\frac{8}{5}=\frac{8}{5}$  

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