Savings Accounts

Question

A father has 4 children each with a savings account. Each account already has money in and the money cannot be transferred between accounts or taken out. Only money can be placed in the accounts at this point. He would like each account to be even based on the age of the child.

The accounts are currently setup with this much money:

• Child 1 - 146 months old, \$1023.61
• Child 2 - 116 months old, \$1260.62
• Child 3 - 99 months old, \$956.20
• Child 4 - 88 months old, \$951.74

What would he have to additionally to each account to keep the ratio of dollars to months of life even amongst the children?

Answer 1

The second child's ratio of money to months is highest, so we can catch the other children up to him or her.

Set $m = 1260.62/116$.

We want to find $x_1, x_3, x_4$ amounts to add for child $1,3$ and $4$, respectively. So we need to solve:

$$ 1023.61 + x_1 = m \times 146 $$ $$ 956.20 + x_3 = m \times 99 $$ $$ 951.74 + x_4 = m \times 88 $$

Solve for $x_1, x_3, x_4$.

Answer 2

Thanks Mark. I'm able to solve, though with a slight change. Child 2 actually has a slightly higher ratio to than child 4. So using child 2 as my m, it works out perfectly.

It will bring them all out to roughly $10.87 per month.

Child 1: $1586.64 Child 2: $1260.62 Child 3: $1075.87 Child 4: $956.33

Thank you!

And sorry for my inability to format these. Ugh!