Question

A pool offers a summer swimming pass with discounted visits. The following equations represent the total cost,
y
, in dollars, of
x
visits to the swimming pool.



Without a summer swimming pass:
y
=
5
x
With a summer swimming pass:
y
=
3
x
+
8


Marco thinks he has determined the number of visits for which the cost will be the same with and without the summer swimming pass.



How can Marco check his solution?

A.
Substitute it in for
x
in both equations and check that both equations have the same
y
-value.

B.
Substitute it in for
y
in both equations and check that both equations have the same
x
-value.

C.
Substitute it in for
x
in both equations and check that one of the equations has a
y
-value of
0
.

D.
Substitute it in for
y
in both equations and check that one of the equations has an
x
-value of
0
.




A pool offers a summer swimming pass with discounted visits. The following equations represent the total cost,
y
, in dollars, of
x
visits to the swimming pool.



Without a summer swimming pass:
y
=
5
x
With a summer swimming pass:
y
=
3
x
+
8


Marco thinks he has determined the number of visits for which the cost will be the same with and without the summer swimming pass.



How can Marco check his solution?

A.
Substitute it in for
x
in both equations and check that both equations have the same
y
-value.

B.
Substitute it in for
y
in both equations and check that both equations have the same
x
-value.

C.
Substitute it in for
x
in both equations and check that one of the equations has a
y
-value of
0
.

D.
Substitute it in for
y
in both equations and check that one of the equations has an
x
-value of
0
.

Answer 1

A.

Marco should substitute his proposed x-value into both equations and check that they give the same y. For example, if x = 4: y = 5(4) = 20 and y = 3(4) + 8 = 20, so the costs are equal.