Question

name: date: formative assessment questions: 1. leila makes $4 per hour and has $30 in her saving account. mark makes $5 per hour and has $5 in his savings account. a. create a linear function that models how much money leila will have in her account after h hours. b. create a linear function that models how much money mark will have in his account after h hours. c. after how many hours will they have the same amount of money? 2. tanya and her younger cousin measure their heights. they notice that tanya is 6 inches taller, and their heights add up to exactly 100 inches. if the variables represent each person’s height, y = tanya’s height and x = cousin’s height, solve the system of equations by using substitution to determine the height of tanya. y = x + 6 and x + y = 100

Explanation:

Step1: Define Leila's linear function

Linear form: $y = mx + b$, where $m=4$, $b=30$.
$L(h) = 4h + 30$

Step2: Define Mark's linear function

Linear form: $y = mx + b$, where $m=5$, $b=5$.
$M(h) = 5h + 5$

Step3: Set functions equal, solve for $h$

Set $4h + 30 = 5h + 5$
$30 - 5 = 5h - 4h$
$h = 25$

Step4: Substitute $y$ into height equation

Substitute $y = x + 6$ into $x + y = 100$:
$x + (x + 6) = 100$

Step5: Solve for $x$, find $y$

$2x + 6 = 100$
$2x = 94$
$x = 47$
$y = 47 + 6 = 53$

Answer:

1. a. $L(h) = 4h + 30$

b. $M(h) = 5h + 5$
c. 25 hours

1. Tanya's height is 53 inches