Answer:64−3X dollars.
Step-by-step explanation:
Let's denote the amount you spent at Banana Republic as
�
B dollars. According to the given information:
You spent
�
X dollars at American Eagle, which is $4 more than the amount spent at Banana Republic, so the amount spent at American Eagle is
�
+
4
B+4 dollars.
You spent $15 less at American Eagle than at Cole Haan, so the amount spent at Cole Haan is
�
+
4
+
15
=
�
+
19
B+4+15=B+19 dollars.
Now, let's calculate the total amount spent:
Total spent
=
�
+
(
�
+
4
)
+
(
�
+
19
)
Total spent=B+(B+4)+(B+19)
Given that you entered the mall with $75:
75
−
Total spent
=
75
−
[
�
+
(
�
+
4
)
+
(
�
+
19
)
]
75−Total spent=75−[B+(B+4)+(B+19)]
Simplify the expression:
75
−
Total spent
=
75
−
(
3
�
+
23
)
75−Total spent=75−(3B+23)
Now, we want to find the remaining amount in terms of
�
X. Since
�
=
�
+
4
X=B+4, substitute
�
=
�
−
4
B=X−4 into the equation:
75
−
(
3
(
�
−
4
)
+
23
)
75−(3(X−4)+23)
Simplify further:
75
−
(
3
�
−
12
+
23
)
75−(3X−12+23)
75
−
(
3
�
+
11
)
75−(3X+11)
Now distribute the negative sign:
75
−
3
�
−
11
75−3X−11
Combine like terms:
64
−
3
�
64−3X
So, the remaining amount in terms of
�
X is
64
−
3
�
64−3X dollars.
