Answer:The concession stand sold
46
hot dogs and
32
hamburgers.
Step-by-step explanation:
The first thing to do in algebraic problems is assign variables to things we don't know, so let's start there:
We don't know how many hot dogs the concession stand sold, so we will call that number
d
.
We don't know how many hamburgers the concession stand sold, so we will call that number
h
.
Now we translate the statements into algebraic equations:
The number of hot dogs and hamburgers that were sold is
78
, so
d
+
h
=
78
.
If each hot dog is sold for
1.25
, then the total revenue from hot dogs is given by
1.25
d
. In the same way, the total revenue from hamburgers is
1.50
h
. The total revenue from both hot dogs and hamburgers should be the sum of these, and since we are told the total revenue is
105.50
, we can say
1.25
d
+
1.5
h
=
105.5
.
We now have a system of two linear equations:
d
+
h
=
78
1.25
d
+
1.5
h
=
105.5
We can solve it using several methods, though I'm going to go with substitution. Use the first equation to solve for
d
:
d
+
h
=
78
→
d
=
78
−
h
Now plug this in for
d
in the second equation:
1.25
d
+
1.5
h
=
105.5
→
1.25
(
78
−
h
)
+
1.5
h
=
105.5
Solving for
h
, we have:
97.5
−
1.25
h
+
1.5
h
=
105.5
0.25
h
=
8
h
=
8
.25
→
h
=
32
Since
h
+
d
=
78
,
32
+
d
=
78
→
d
=
46
Step-by-step explanation: