Question

select the correct answer.
a dj tracks the song requests she receives on a friday night. she noted that the number of requests for country songs was 2 more than \\( \frac{4}{3} \\) times the number of requests for hip - hop songs. there were 18 requests for country. if \\( x \\) represents the number of requests for hip - hop songs, which equation represents this situation? how many requests for hip - hop songs did the dj receive on friday night?
a. the equation is \\( \frac{4}{3}x + x + 2 = 18 \\), and the number of hip - hop songs is 48.
b. the equation is \\( \frac{4}{3}x + 2 = 18 \\), and the number of hip - hop songs is 12.
c. the equation is \\( \frac{4}{3}+2x = 18 \\), and the number of hip - hop songs is 36.
d. the equation is \\( \frac{4}{3}x + 2x = 18 \\), and the number of hip - hop songs is 20.
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Explanation:

Step1: Define country song equation

Let $x$ = hip-hop requests. Country requests: $\frac{4}{3}x + 2 = 18$

Step2: Isolate the term with $x$

Subtract 2 from both sides:
$\frac{4}{3}x = 18 - 2$
$\frac{4}{3}x = 16$

Step3: Solve for $x$

Multiply both sides by $\frac{3}{4}$:
$x = 16 \times \frac{3}{4}$
$x = 12$

Answer:

B. The equation is $\frac{4}{3}x + 2 = 18$, and the number of hip-hop songs is 12.