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.

1) name the variables:

 - amount in account 1 "a"
 - amount in account 2 "b"

2) trtanslate the statements into equations:

- the difference between account 1 and account 2 is $100.

=> a - b = 100

-  if she uses 3/8 of account 1 and 7/8 of account 2, Dawn will have a down payment of $2,000.

=> (3/8)a + (7/8)b = 2000

3) solve the system of equations

(1) a - b = 100
(2) (3/8)a + (7/8b) = 2000

Steps:

- multiply equation (1) by 7 and equaton (2) by 8

=>

(1) 7a - 7b = 700
(2) 3a + 7b = 16,000

- add the two equations

=>

7a + 3a - 7b + 7b = 700 + 16,000

- combine like terms:

10a = 16,700

- divide by 10:

a = 16,700 / 10 = 1670

- use equation (1) to find b:

a - b = 100 => b = a - 100 = 1670 - 100 = 1570

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