Answer:
4 jars
Step-by-step explanation:
Elizabeth has already earned $95.00 from jam sales and $24.00 from leading a demonstration, so she only needs to earn an additional $331 to reach her goal of $450.00.
To find the minimum number of jars Elizabeth must sell to reach her goal, we can use the formula for calculating the sum of a geometric series:
(1st term x (1 - r^n) / (1 - r))
where n is the number of terms in the series (in this case, jars of jam) and r is a constant representing the "common ratio" of the series (in this case, the "common ratio" is the amount by which each jar is sold).
Substituting the values we know, we get:
(first term x (1 - r^n) / (1 - r)) = 331
First term = 95/5 = 19
1 - r^n = 1 - (2/3)^n
1 - r = 1 - (1 - 2/3)
1 - r = (2/3)
Substituting these values into the formula:
(first term x (1 - r^n) / (1 - r)) = 331
19 x (1 - (2/3)^n) / (1 - (2/3)) = 331
19 x ((2/3)^n - 1) / (2/3) = 331
From here, we can see that n must be greater than or equal to 3 to make both the numerator and denominator positive. To find the smallest value of n that satisfies this condition, we can use the fact that (2/3)^3 is approximately equal to 0.435, so n must be greater than or equal to 4. Therefore, the minimum number of jars Elizabeth must sell to reach her goal is 4 jars.
