Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day. (4 points)
What equation represent how much money Judy will have in total after saving for d days?
What equation represents how much money Elenore will have in total after saving for d days?
What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved?
After the number of days it took both to have the same amount of money saved, how much money do they have each?
The equation that represents how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + ($5 * d)
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + ($7 * d)
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
$100 + ($5 * d) = $75 + ($7 * d)
After the number of days it took both to have the same amount of money saved, they will each have $175.
The equation that represents how much money Judy will have in total after saving for d days is:
Judy's Total Savings = Initial Amount + (Savings per day)(Number of days)
Judy's Total Savings = $100 + ($5)(d)
Judy's Total Savings = $100 + $5d
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's Total Savings = Initial Amount + (Savings per day)(Number of days)
Elenore's Total Savings = $75 + ($7)(d)
Elenore's Total Savings = $75 + $7d
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's Total Savings = Elenore's Total Savings
$100 + $5d = $75 + $7d
After the number of days it took both to have the same amount of money saved, we can solve the equation to find the value of d. Once we have the value of d, we can substitute it back into either equation to find out how much money they each have.
To answer these questions, we can use the following equations and steps:
1. Equation for Judy's total savings after d days:
Judy's initial amount + (Judy's savings per day × number of days) = Judy's total savings
100 + (5 × d) = Judy's total savings
2. Equation for Elenore's total savings after d days:
Elenore's initial amount + (Elenore's savings per day × number of days) = Elenore's total savings
75 + (7 × d) = Elenore's total savings
3. Equation to find out how many days it will take for Judy and Elenore to have the same amount of money saved:
Set Judy's total savings equal to Elenore's total savings and solve for d:
100 + (5 × d) = 75 + (7 × d)
4. After finding the value of d in step 3, substitute it back into either Judy's or Elenore's equation to calculate how much money they have each. For example, using Judy's equation:
Judy's total savings = 100 + (5 × d)
Now, let's calculate the answers using the equations:
1. Judy's total savings after d days: 100 + (5 × d)
2. Elenore's total savings after d days: 75 + (7 × d)
3. To find the number of days it will take for Judy and Elenore to have the same amount of money saved:
100 + (5 × d) = 75 + (7 × d)
100 - 75 = (7 × d) - (5 × d)
25 = 2 × d
d = 12.5 days
Since we cannot have a fraction of a day, we can round up to the nearest whole number. Therefore, it will take 13 days for Judy and Elenore to have the same amount of money saved.
4. After 13 days, Judy's total savings would be:
100 + (5 × 13) = $165
After 13 days, Elenore's total savings would be:
75 + (7 × 13) = $164
Therefore, after 13 days, Judy would have $165 and Elenore would have $164.