Question

solving equations with addition and subtraction

1. one day, ryan puts five $1.00 bills into a jar. each day after that, he adds $1.00 to the jar.

chart showing dollars in the jar on day 1, day 2, day 3
a. on what day does ryan have $100.00 in the jar? how do you know?
b. how many dollars does ryan have in the jar on day 100? how do you know?

Explanation:

Step1: Define linear equation

Let $d$ = day number, $A$ = total amount.
The amount follows: $A = 5 + (d - 1)$
Simplify: $A = d + 4$

Step2: Solve for day with $100$

Set $A=100$, solve for $d$:
$100 = d + 4$
$d = 100 - 4$
$d = 96$

Step3: Calculate day 100 amount

Use $A = d + 4$, substitute $d=100$:
$A = 100 + 4$
$A = 104$

Answer:

a. Day 96. Using the linear equation for the total amount $A = d + 4$, setting $A=100$ gives $d=96$.
b. $\$104$. Using the linear equation $A = d + 4$, substituting $d=100$ gives $A=104$.