Answer:
The relationship between the number of gems and the number of chests can be represented by an equation in the form of g = kc, where g is the number of gems, c is the number of chests, and k is a constant.
To find the value of the constant k, we can substitute the values from one of the adventures into the equation and solve for k. For example, using the values from Adventure A:
g = 600
c = 2
Substituting these values into the equation, we get:
600 = k * 2
Solving for k, we get:
k = 600 / 2 = 300
Therefore, the equation that describes the relationship between the number of gems and the number of chests is:
g = 300c
Using the information provided in the table, we know that for Adventure B, Lulu received 1500 gems and needed 5 chests to hold them. Substituting these values into the equation, we get:
g = 1500
c = 5
Substituting these values into the equation g = 300c, we get:
1500 = 300 * 5
This equation can be used to determine the number of chests needed to hold a given number of gems, or vice versa. For example, to find the number of chests needed to hold 1200 gems, we can substitute 1200 for g and solve for c:
g = 1200
c = 1200 / 300 = 4
Thus, 4 chests would be needed to hold 1200 gems.