Danny, amira, and tyler shared a sum of money in the ratio 6 : 4 : 3. amira used 1/2 of her money to buy a watch that costs $30, and danny gave 1/3 of his money to his sister. how much money did they have left altogether?

$135

Step-by-step explanation:

step 1

Let

x> amount of money shared by Danny

y> amount of money shared by Amira

z> amount of money shared by Tyler

we know that

x/y=6/4 > x=1.5y > equation A

x/z=6/3 ---> z=x/2 ---> equation B

Amira used 1/2 of her money to buy a watch that costs $30

so

(1/2)y=$30

y=$60

Substitute the value of y in the equation A and solve for x

x=1.5y > x=1.5(60)=$90

Substitute the value of x in the equation B and solve for z

z=x/2 > z=90/2=$45

so

The amount of money shared by Danny was $90

The amount of money shared by Amira was $60

The amount of money shared by Tyler was $45

step 2

Find out how much money they have left in total.

Danny gave 1/3 of his money to his sister > left --> (2/3)($90)=$60

Amira used 1/2 of her money > left --> $60/2=$30

Tyler > left > $45

Total=$60+$30+$45=$135