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

Question

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

Answer 1

To find the total number of grams of sugar Lana will use to make the first 6 batches of muffins, we need to calculate the sum of the sugar used in each batch.

The sugar used in the first batch is 500 grams.

In the second batch, Lana uses three-fourths as much sugar, which is (3/4)*500 = 375 grams.

In the third batch, Lana uses three-fourths as much sugar as she used in the second batch, which is (3/4)*375 = 281.25 grams.

In the fourth batch, Lana uses three-fourths as much sugar as she used in the third batch, which is (3/4)*281.25 = 210.9375 grams.

In the fifth batch, Lana uses three-fourths as much sugar as she used in the fourth batch, which is (3/4)*210.9375 = 158.203125 grams.

In the sixth batch, Lana uses three-fourths as much sugar as she used in the fifth batch, which is (3/4)*158.203125 = 118.65234375 grams.

To find the total, we sum up the sugar used in each batch: 500 + 375 + 281.25 + 210.9375 + 158.203125 + 118.65234375.

Simplifying the expression, we get the sum to be 1643.04296875.

Therefore, the expression Lana can use to find the total number of grams of sugar she will use to make the first 6 batches of muffins is 1643.04296875.