Question

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?

Answer 1

$135

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