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

240 : (3+2) = 48

then 

$5 = 48 x 3
$10 = 48 x 2

A) the number of 10 = 96
B) ratio = 144 - 96 = 48 

Total piece of notes = 240
$5 notes = x
$10 notes = y
Ratio of number = x : y = 3 : 2

x : y = 3 : 2
2x = 3y
x = ³/₂ y

a. The number of $10 (y = ?) 
[tex]x+y=240 \\ \\ \frac{3}{2}y+y=240 \\ \\ \frac{3}{2}y+ \frac{2}{2}y=240 \\ \\ \frac{5}{2}y=240 \\ \\ y=240 \times \frac{2}{5} \\ \\ y= 48 \times 2 \\ \\ y=96[/tex]

So, the number of $10 are 96 pieces

b. The ratio of value (value of $5 : value of $10)

The number of $5 (x)
x + y = 240
x = 240 - y
x = 240 - 96
x = 144 pieces

The ratio is
= (144 × $5) : (96 × $10)
= $720 : $960............both sides are devided by $240
= ($720/$240) : ($960/$240)
= 3 : 4

So, the ratio of the value of the $5 notes to that of the $10 notes is 3 : 4