Question
Levi is making coasters with two different designs to sell at a craft show. Each design uses some metallic beads. Design A uses
4
silver beads and
7
gold beads. Design B uses
6
silver beads and
6
gold beads. Levi only has
48
silver beads and
66
gold beads left. The number of coasters of design
a
and
b
that Levi can make is represented by the following system of inequalities.
{
4
a
+
6
b
≤
48
7
a
+
6
b
≤
66
Which graph and interpretation BEST represent the situation?
A.
Levi can make up to
6
coasters of design A.
image
B.
Levi can make up to
9
coasters of design A.
image
C.
Levi can make up to
4
coasters of design B.
image
D.
Levi can make up to
11
coasters of design B.
image
4
silver beads and
7
gold beads. Design B uses
6
silver beads and
6
gold beads. Levi only has
48
silver beads and
66
gold beads left. The number of coasters of design
a
and
b
that Levi can make is represented by the following system of inequalities.
{
4
a
+
6
b
≤
48
7
a
+
6
b
≤
66
Which graph and interpretation BEST represent the situation?
A.
Levi can make up to
6
coasters of design A.
image
B.
Levi can make up to
9
coasters of design A.
image
C.
Levi can make up to
4
coasters of design B.
image
D.
Levi can make up to
11
coasters of design B.
image
Answers
GPT-5 mini
Answer: B.
Reason: Set b = 0 to maximize a. From 4a ≤ 48 we get a ≤ 12; from 7a ≤ 66 we get a ≤ 66/7 ≈ 9.43. Both must hold, so a ≤ 66/7, i.e. at most 9 whole coasters of design A.
Reason: Set b = 0 to maximize a. From 4a ≤ 48 we get a ≤ 12; from 7a ≤ 66 we get a ≤ 66/7 ≈ 9.43. Both must hold, so a ≤ 66/7, i.e. at most 9 whole coasters of design A.