Question

At the beginning of the year, Jace had $55 in savings and saved an additional $19 each week thereafter. Evelyn started the year with $85 and saved $14 every week. Let JJ represent the amount of money Jace has saved tt weeks after the beginning of the year and let EE represent the amount of money Evelyn has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t, commat, and determine the who has more money saved after 4 weeks.

Answer 1

To formulate the equations for Jace and Evelyn's savings, we can express their total savings as functions of time in weeks (t).

1. **Jace's Savings (JJ)**:
Jace starts with $55 and saves an additional $19 each week. Thus, his total savings after \( t \) weeks can be expressed as:
\[
JJ(t) = 55 + 19t
\]

2. **Evelyn's Savings (EE)**:
Evelyn starts with $85 and saves an additional $14 each week. Therefore, her total savings after \( t \) weeks is given by:
\[
EE(t) = 85 + 14t
\]

Next, we will evaluate how much money each of them has saved after 4 weeks, by substituting \( t = 4 \) into their equations:

1. **Calculating Jace's Savings After 4 Weeks**:
\[
JJ(4) = 55 + 19 \cdot 4 = 55 + 76 = 131
\]

2. **Calculating Evelyn's Savings After 4 Weeks**:
\[
EE(4) = 85 + 14 \cdot 4 = 85 + 56 = 141
\]

Now, we compare their savings after 4 weeks:
- Jace has saved $131.
- Evelyn has saved $141.

Therefore, **Evelyn has more money saved after 4 weeks**.