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?
1) The equation that represents how much money Judy will have in total after saving for d days is: 100 + 5d.
2) The equation that represents how much money Elenore will have in total after saving for d days is: 75 + 7d.
3) 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 + 5d = 75 + 7d.
4) After the number of days it took both to have the same amount of money saved, the amount of money they each have can be found by substituting the value of d into either of their equations.
To answer these questions, we need to understand the equations for calculating the total amount of money saved by Judy and Elenore after a certain number of days.
1. Equation for Judy's savings:
The amount of money Judy has after saving for d days can be represented by the equation:
Judy's savings = Initial amount + (Savings per day x Number of days)
Thus, the equation would be:
Judy's savings = $100 + ($5 x d)
2. Equation for Elenore's savings:
Similarly, the equation for Elenore's savings after d days would be:
Elenore's savings = $75 + ($7 x d)
3. Equation to find the number of days needed for both to have the same amount of money saved:
To find the number of days it will take for Judy and Elenore to have the same amount of money saved, we need to set their savings equal to each other:
$100 + ($5 x d) = $75 + ($7 x d)
Simplifying the equation:
$5d - $7d = $75 - $100
-$2d = -$25
Dividing both sides by -2:
d = 12.5
Since we cannot have half days, we round up to the next whole number.
Therefore, it would take 13 days for Judy and Elenore to have the same amount of money saved.
4. Amount of money after they have the same savings:
To find out how much money Judy and Elenore have each after 13 days, we substitute the value of d into the equations:
Judy's savings after 13 days:
Judy's savings = $100 + ($5 x 13)
Judy's savings = $100 + $65
Judy's savings = $165
Elenore's savings after 13 days:
Elenore's savings = $75 + ($7 x 13)
Elenore's savings = $75 + $91
Elenore's savings = $166
After 13 days, Judy would have $165 and Elenore would have $166.
1. The equation that represents how much money Judy will have in total after saving for d days is:
Judy's Total Savings = $100 + $5 * d
2. The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's Total Savings = $75 + $7 * d
3. 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
4. After the number of days it took both to have the same amount of money saved, they will have the same amount of money. To find the amount, substitute the number of days into any of the equations and solve for the total savings. For example, if it took 20 days for them to have the same amount of money saved, substitute d = 20 into either equation:
Judy's Total Savings = $100 + $5 * 20 = $100 + $100 = $200
Elenore's Total Savings = $75 + $7 * 20 = $75 + $140 = $215
After 20 days, Judy would have $200 and Elenore would have $215.