Question

A club is raising funds by selling bracelets and keychains. On Saturday, the club sold a total of
14
keychains and bracelets combined. Each bracelet earned a profit of
$
4
, but due to material costs, each keychain resulted in a loss of
$
2
. The club earned a total profit of
$
20
on Saturday.



A student claims that solving the following system of equations determines the number of bracelets and keychains sold on Saturday, where
k
represents the number of keychains and
b
represents the number of bracelets.



k
=
b
−
14

4
b
−
2
k
=
20



What error did the student make in writing the system of equations?

A.
The first equation is incorrect. It should be
k
−
b
=
14
.

B.
The first equation is incorrect. It should be
k
=
−
b
+
14
.

C.
The second equation is incorrect. It should be
4
b
+
2
k
=
20
.

D.
The second equation is incorrect. It should be
2
b
−
4
k
=
20
.

Answer 1

B.

The total number sold gives k + b = 14, so k = 14 − b (which is k = −b + 14). The second equation 4b − 2k = 20 is correct (bracelets give +$4 each, keychains −$2 each).