Question

Bo paid bills with 1/2 of his paycheck snd put 1/5 of the remainder in savings. The rest of his paycheck he divided equally among the college accounts of his 3 children.

A. what fraction of his paycheck went into each childs account?
B. If Bo deposited $400 in each childs account, how much money was in Bo's original paycheck?

Answer 1

1/2 + 1/5(1/2) = 1/2 + 1/10 = 5/10 + 1/10 = 6/10....this leaves 4/10 (reduces to 2/5) for his children.

(2/5) / 3 = 2/5 * 1/3 = 2/15 for each child <== A

400 in each childs account.....thats (400 * 3) = 1200 ...
2/5 of what is 1200 =
2/5x = 1200
x = 1200 * 5/2
x = 6000/2
x = 3000 <== B

check...
total pay is 3000
1/2 for bills.....- 1500
1/5(-1500) = -1500/5 = -300 ....for savings
3000 - (1500 + 300) = 3000 - 1800 = 1200...remaining for the children
1200/3 = 400 ...for each child.

so ur answers are :
A. 2/15 in each childs account
B. original paycheck = $ 3000

Answer 2

Bo's original paycheck is $3000.

Explanation:

Bo paid bills with 1/2 of his paycheck and put 1/5 of the remainder in savings.

The rest of his paycheck he divided equally among the college accounts of his 3 children.

Let his earnings be x

So,
`x-(1)/(2)`went in bills.

And he put 1/5 of the remainder in savings.

`(1)/(5)((1)/(2) ) =(1)/(10)`

He put
`(1)/(10)` of x in savings

Adding the bill and remainder amount =
`(1)/(2) +(1)/(0)`

=
`(5+1)/(10)=(6)/(10)`

So, left amount was =
`1-(6)/(10)=(10-6)/(10)=(4)/(10)=(2)/(5)`

This 2/5 was divided equally among 3 kids making it :

`((2)/(5) )/(3) =(2)/(15)`

Now, as given, Bo deposited $400 in 3 kids accounts. This gives
`3*400=1200` in total in kids account.

We know $1200 is 2/5 of total income or x

So,
`(2x)/(5)=1200`

`2x=6000`

x = $3000

Hence, Bo's original paycheck is $3000.