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 us es 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.
2 answers:
1) name the variables: - amount in account 1 "a" - amount in account 2 "b" 2) trtanslate the statements into equations: <span>- 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 = 1570Answer: Dawn has $ 1670 in account 1 and
$ 1570 in account 2.
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Answer: Dawn has $1670 in account 1 and $1570 in account 2.
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