Question

sonia opened a savings account and then added the same amount to the savings account every week. after 5 weeks, her savings account had a total of $45. after 10 weeks, her savings account had a total of $70. which equation represents the amount of money (y), in dollars, in sonias savings account after x weeks?
$y = 7x$
$y = 9x$
$y = 5x + 20$
$y = 20x + 5$

Explanation:

Step1: Define linear equation form

The relationship follows $y = mx + b$, where $m$ is weekly deposit, $b$ is initial amount.

Step2: Set up two equations

From given data:

1. After 5 weeks: $45 = 5m + b$
2. After 10 weeks: $70 = 10m + b$

Step3: Solve for $m$

Subtract first equation from second:
$$70 - 45 = (10m + b) - (5m + b)$$
$$25 = 5m$$
$$m = \frac{25}{5} = 5$$

Step4: Solve for $b$

Substitute $m=5$ into $45 = 5m + b$:
$$45 = 5(5) + b$$
$$45 = 25 + b$$
$$b = 45 - 25 = 20$$

Step5: Form final equation

Substitute $m=5$, $b=20$ into $y=mx+b$.

Answer:

y = 5x + 20