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:
@@MATH_TOKEN_2@@ 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
