there are a total of 240 pieces of $5 notes and $10 notes.The numbers of $5 and $10notes are in the ratio 2:3 find the number of $5 notes

$5 notes = x
$10 notes = y

x : y = 2 : 3 ⇒ 3x = 2y ⇒ x = ²/₃ y

x + y = 240

[tex]\frac{2}{3}y+y=240 \\ \\ \frac{2}{3}y+ \frac{3}{3}y=240 \\ \\ \frac{5}{3}y=240 \\ \\ y=240 \times \frac{3}{5} \\ \\ y= 48 \times 3 \\y= 144 \\ \\ \\ x+y=240 \\ x+144=240 \\ x=240-144 \\ x=96 \\ \\ So,\ the\ number\ of\ \$ 5\ notes\ are\ 96\ pieces. [/tex]