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

Answer

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:

$\frac{3}{8} a+\frac{7}{8} b=2000$ 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 $b$

$\frac{3}{8} (100+b)+\frac{7}{8} b=2000$

$37.5 +\frac{3}{8} b+\frac{7}{8} b=2000$

$\frac{5}{4} b=1962.5$

$b=1570$ 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

Answer 2

Answer:

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

Step-by-step explanation:

Ed2020