Answer: $80
Step-by-step explanation:
Let's represent the functions for the savings of Kayden (
�
(
�
)
K(t)) and Mia (
�
(
�
)
M(t)) in terms of the number of weeks (
�
t).
For Kayden:
�
(
�
)
=
60
+
5
�
K(t)=60+5t
For Mia:
�
(
�
)
=
40
+
10
�
M(t)=40+10t
Now, you can graph these functions to visualize the savings over time.
To find the week when they have the same amount saved (
�
(
�
)
=
�
(
�
)
K(t)=M(t)), set the two equations equal to each other and solve for
�
t:
60
+
5
�
=
40
+
10
�
60+5t=40+10t
Subtract 40 from both sides:
20
+
5
�
=
10
�
20+5t=10t
Subtract 5t from both sides:
20
=
5
�
20=5t
Divide by 5:
�
=
4
t=4
So, after 4 weeks, Kayden and Mia will have the same amount of money saved. To find the amount saved at that time, plug
�
=
4
t=4 into either
�
(
�
)
K(t) or
�
(
�
)
M(t). Let's use
�
(
�
)
K(t):
�
(
4
)
=
60
+
5
×
4
=
80
K(4)=60+5×4=80
Therefore, after 4 weeks, both Kayden and Mia will have saved $80.
