Question

Red is baking bread, the dough grows in size by 15 percent every ten minutes. If she needs 1950 millimeters to fill the pan after 1 hour how much dough must she begin with.

Answer 1

Answer: 843.0388 millimeters approximately

Explanation

There are 6 ten minute periods in 1 hour.

The multiplier 1.15 represents 15% growth.

The equation to solve is

P*(1.15)^6 = 1950

Divide both sides by (1.15)^6 and we get

P = 1950/( (1.15)^6 ) = 843.0388 approximately

Round this value however needed.

Answer 2

Red must begin with approximately 1026.32 millimeters of dough.

Explanation:

To determine the amount of dough Red must begin with, we need to calculate the growth rate of the dough over 1 hour.

Given that the dough grows in size by 15% every ten minutes, we can express the growth rate as a decimal by dividing it by 100:

Growth rate per ten minutes = 15% = 15/100 = 0.15

Since there are 6 sets of ten minutes in 1 hour, the total growth rate over 1 hour is:

Total growth rate over 1 hour = Growth rate per ten minutes * Number of sets of ten minutes in 1 hour

Total growth rate over 1 hour = 0.15 * 6 = 0.9

Now, we can set up the equation to find the initial amount of dough that Red must begin with:

Initial amount of dough * (1 + Total growth rate over 1 hour) = Amount of dough needed to fill the pan

Let's solve for the initial amount of dough:

Initial amount of dough * (1 + 0.9) = 1950 millimeters

Simplifying the equation:

Initial amount of dough * 1.9 = 1950

Dividing both sides of the equation by 1.9:

Initial amount of dough = 1950 / 1.9

Calculating the value:

Initial amount of dough ≈ 1026.32 millimeters