Lana follows a recipe to make muffins. She finds they are too sweet, so in the next batch, she uses three-fourths as much sugar. She continues refining the recipe by using three-fourths as much sugar in each successive batch. If she used 500 grams of sugar in the first batch, which expression can Lana use to find the total number of grams of sugar she will use to make the first 6 batches of muffins?
The total amount of sugar Lana used in each batch is decreasing by three-fourths each time. To find the total amount of sugar she uses for the first 6 batches, we can use a geometric sequence.
The first term in the sequence is 500 grams of sugar, and the common ratio is three-fourths (or 3/4).
Thus, the expression to find the total amount of sugar used in the first 6 batches is:
500 + (500 * (3/4)) + (500 * (3/4)^2) + (500 * (3/4)^3) + (500 * (3/4)^4) + (500 * (3/4)^5)
which one of the following is right 500(1-(3/4)^6) or 500(1-3/4)/(1-3/4) or 500(1-(3/4)^6)/(1-3/4) or 500(1-(3/4))^6/(1-3/4) ?
The correct expression to find the total amount of sugar used in the first 6 batches is:
500(1 - (3/4)^6)
This expression accounts for the fact that the amount of sugar used in each batch is decreasing by three-fourths each time.
What is (3/4)^6?
To calculate (3/4)^6, you multiply 3/4 by itself six times:
(3/4)^6 = (3/4) * (3/4) * (3/4) * (3/4) * (3/4) * (3/4)
Simplifying this expression, we get:
(3/4)^6 = 729/4096
what's 1-729/4096
To find 1 - 729/4096, we need to have a common denominator. The common denominator for 1 and 729/4096 is 4096.
Converting 1 to have a denominator of 4096, we get:
1 = 4096/4096
Therefore, the expression becomes:
4096/4096 - 729/4096
Simplifying the expression, we get:
(4096 - 729) / 4096 = 3367/4096
what's 3367/4096 times 500
To calculate 3367/4096 multiplied by 500, you multiply the numerators and denominators:
(3367/4096) * 500 = (3367 * 500) / (4096).
Multiplying the numerators, we get:
3367 * 500 = 1,683,500.
The denominator remains the same:
(1,683,500 / 4096).