Question

sarah is saving up to buy a new snowboard and boots for the winter that costs $850. she has already saved some money and babysits each week. after 2 weeks, she has saved up $305 and after 5 weeks she has $560. how much money did she start with (initial value)? $135 $305 $850 i do not know the answer yet. $0

Explanation:

Step1: Define variables

Let $b$ = initial savings, $m$ = weekly savings.

Step2: Set up linear equations

After 2 weeks: $2m + b = 305$
After 5 weeks: $5m + b = 560$

Step3: Eliminate $b$ (subtract equations)

$(5m + b) - (2m + b) = 560 - 305$
$3m = 255$

Step4: Solve for $m$

$m = \frac{255}{3} = 85$

Step5: Solve for initial $b$

Substitute $m=85$ into $2m + b = 305$:
$2(85) + b = 305$
$170 + b = 305$
$b = 305 - 170 = 135$

Answer:

$135$