Question

the ratio of rock songs to country songs on tony’s spotify playlist is 5:6. the total number of rock and country songs tony has is between 100 and 120. how many rock songs does he have?
just look at the original ratio first, 5:6. how many total songs would that be? blank total songs.
now think of a multiple of that number you just came up with that would fit between 100 and 120. blank. this is the total number of songs that tony has. of that number, how many rock songs would he have if his ratio of rock songs to country songs is 5:6? blank rock songs

Explanation:

Step1: Find total parts in ratio

The ratio of rock to country songs is \(5:6\). To find the total number of parts, we add the two parts of the ratio: \(5 + 6 = 11\). So, the total number of songs in one "set" of the ratio is \(11\) songs.

Step2: Find multiple of 11 between 100 and 120

We need to find a multiple of \(11\) that lies between \(100\) and \(120\). Let's list the multiples of \(11\): \(11\times9 = 99\), \(11\times10 = 110\), \(11\times11 = 121\). Among these, \(110\) is between \(100\) and \(120\). So, the total number of songs is \(110\).

Step3: Calculate number of rock songs

The ratio of rock songs to total songs is \(\frac{5}{11}\) (since there are \(5\) parts of rock and \(11\) total parts). To find the number of rock songs, we multiply the total number of songs by this fraction: \(110\times\frac{5}{11}= 50\).

Answer:

First box: \(11\)
Second box: \(110\)
Third box: \(50\)