Question

Altogether Central High School's bands have 40 trumpets and 35 tubas. Carlee says the ratio of trumpets to tubas is 40:35. Danny disagrees and says the ratio is 8:7.

Actually, they are both correct. Explain why these are equivalent ratios.

Answer 1

Explanation is given below.

Explanation:

Given:

Number of Trumpets = 40

Number of tubas = 35

Carlee says, the ratio of trumpets to tubas = 40 : 35

Danny says, the ratio of trumpets to tubas = 8 : 7

To explain why the two ratios are equivalent.

Solution:

Equivalent ratios are all ratios which are equal to each other in their reduced to simplest form.

The ratio of trumpets to tubas can be given as =
`(40)/(35)`

To reduce the ratio to its simplest form, we divide both numbers by their G.C.F.

The G.C.F. for 40 and 35 is 5.

So, we divide numerator and denominator by 5.

⇒
`(40/5)/(35/ 5)`

⇒
`(8)/(7)`

Thus, the simplest ratio of trumpets to tubas can be given as = 8:7

This is why both Danny and Carlee are correct with the ratios of trumpets to tubas.

Carlee gave the direct ratio, while Danny gave the simplest ratio.