Question

Dawn has been using two bank accounts to save money for a car. the difference between account 1 and account 2 is $100. if she uses 3/8 of account 1 and 7/8 of account 2, dawn will have a down payment of $2,000. solve the system of equations to find the total amount of money dawn has in each account. a – b = 100 a b = 2,000 dawn has $ in account 1 and $ in account 2.

Answer 1

Dawn has $1670 in account 1 and $1570 in account 2

Explanation:

Ed2020

Answer 2

Dawn has $1670 in account 1 and $1570 in account 2

Explanation

Let
`a` be the amount of money in account 1

Let
`b` be the amount of money in account 2

We know from our problem that the difference between account 1 and account 2 is $100, so:

`a-b=100` equation (1)

We also know that if she uses 3/8 of account 1 and 7/8 of account 2, dawn will have a down payment of $2,000, so:

`(3)/(8) a+(7)/(8) b=2000` equation (2)

Now let's solve our system of equations (1) and (2) step by step:

Step 1. Solve for
`a` in equation (1)

`a-b=100`

`a=100+b` equation (3)

Step 2. Replace equation (3) in equation (2) and solve for
`b`

`(3)/(8) (100+b)+(7)/(8) b=2000`

`37.5 +(3)/(8) b+(7)/(8) b=2000`

`(5)/(4) b=1962.5`

`b=1570` equation (4)

Step 3. Replace equation (4) in equation (3)

`a=100+1570`

`a=1670`

Dawn has $1670 in account 1 and $1570 in account 2