The total value of the coins is 50 cents.
Since the table shows a linear relationship between the number of nickels and the total value of the coins, we can write the relationship as an equation of the form:
c = mn + b
where:
c is the total value of the coins in cents
m is the slope of the line
n is the number of nickels
b is the y-intercept
We can use the two data points in the table to solve for m and b. Using the point (6, 40), we get:
40 = 6m + b
Using the point (7, 45), we get:
45 = 7m + b
Subtracting the first equation from the second equation, we get:
5 = m
Substituting 5 for m in the first equation, we get:
40 = 6(5) + b
40 = 30 + b
b = 10
Therefore, the equation of the relationship is:
c = 5n + 10
If Janelle has 8 nickels in her coin purse, then the total value of the coins is:
c = 5(8) + 10
c = 40 + 10
c = 50
Therefore, the total value of the coins is 50 cents.