The number of gallons g in a swimming pool being filled with water is g = 50x + 1,000, where x is the number of hours since sunrise. It has been 10 hours since sunrise. What is the initial value?

Question

__ gallons

Answer 1

To find the initial value (the number of gallons in the pool at the beginning, x = 0), we can substitute x = 0 into the equation:

g = 50(0) + 1,000
g = 0 + 1,000
g = 1,000

Therefore, the initial value is 1,000 gallons.

Answer 2

Days Fine
2 30 cents
3 45 cents
4 60 cents
The tables shows the fine owed for an overdue library book according to how many days it is overdue. What is the initial value?
__ cent

Answer 3

To find the initial value (the fine amount for 0 days overdue), we can use the formula for a linear relationship:

Fine = mx + b

We can use the data provided to determine the initial value. Let's take the data for 2 days overdue as an example:

When the book is 2 days overdue:
Fine = 2m + b (where m is the fine per day)

From the information given:
When the book is 2 days overdue, the fine is 30 cents:
2m + b = 30

Let's take the data for 3 days overdue as another example:

When the book is 3 days overdue:
Fine = 3m + b

From the information given:
When the book is 3 days overdue, the fine is 45 cents:
3m + b = 45

Now, we can solve these two equations simultaneously to find the values of m and b.

Subtracting the equation of 2m + b = 30 from 3m + b = 45:
(3m + b) - (2m + b) = 45 - 30
m = 15 cents

Substitute m = 15 cents into 2m + b = 30:
2(15) + b = 30
30 + b = 30
b = 0

Therefore, the initial value (fine for 0 days overdue) is 0 cents.

Answer 4

Years Amount
1 $1,080
2 $1,160
3 $1,240
The table shows the amount of money in a bank account after a certain number of years. What is the initial value?
$__

Answer 5

To find the initial value (the amount of money in the bank account at the starting point, year 0), we can use the formula for a linear relationship:

Amount = mx + b

We can use the data provided to determine the initial value. Let's take the data for 1 year as an example:

When the account has been open for 1 year:
Amount = 1m + b (where m is the increase in amount per year)

From the information given:
When the account has been open for 1 year, the amount is $1,080:
1m + b = 1,080

Let's take the data for 2 years as another example:

When the account has been open for 2 years:
Amount = 2m + b

From the information given:
When the account has been open for 2 years, the amount is $1,160:
2m + b = 1,160

Now, we can solve these two equations simultaneously to find the values of m and b.

Subtracting the equation of 1m + b = 1,080 from 2m + b = 1,160:
(2m + b) - (1m + b) = 1,160 - 1,080
m = 80

Substitute m = 80 into 1m + b = 1,080:
1(80) + b = 1,080
80 + b = 1,080
b = 1,000

Therefore, the initial value (the amount of money in the bank account at the beginning) is $1,000.