Question

solving a real - world system of equations
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.
$a - b = 100$
$\frac{3}{8}a+\frac{7}{8}b = 2,000$
dawn has $1,670$ in account 1 and $\square$ in account 2
$1,570$
$1,670$
$4,175$
$4,275$
multiply each equation by a number that produces coefficients for $x$ or $y$.
$1x - 1y = 100$ $\times$...
$\frac{3}{8}x+\frac{7}{8}y = 2000$ $\times$...

Explanation:

Step1: Define variables

Let $A$ = account 1, $B$ = account 2

Step2: Write given equations

$A - B = 100$
$\frac{3}{8}A + \frac{7}{8}B = 2000$

Step3: Eliminate fractions (eq2 ×8)

$3A + 7B = 16000$

Step4: Isolate A from eq1

$A = B + 100$

Step5: Substitute A into new eq2

$3(B + 100) + 7B = 16000$
$3B + 300 + 7B = 16000$
$10B = 15700$

Step6: Solve for B

$B = \frac{15700}{10} = 1570$

Answer:

Dawn has $\$1,670$ in account 1 and $\$1,570$ in account 2.