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 representing how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + $5 * d
The equation representing how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + $7 * d
The equation 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
To solve this equation and find the number of days it will take for Judy and Elenore to have the same amount of money saved, we can rearrange the equation to isolate d:
$5 * d - $7 * d = $75 - $100
-$2 * d = -$25
d = 12.5
Since it is not possible to have half days, we can round up to the nearest whole number, which means it will take 13 days for them to have the same amount of money saved.
After 13 days, both Judy and Elenore will have the same amount of money saved. To find out how much money they each have, we can substitute the value of d into one of the original equations. Let's use Judy's equation:
Judy's total money = $100 + $5 * 13
Judy's total money = $100 + $65
Judy's total money = $165
Therefore, Judy and Elenore will each have $165 saved after 13 days.
The equation that represents how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + ($5 per day × d days)
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + ($7 per day × d days)
To find out how many days it will take for Judy and Elenore to have the same amount of money saved, we need to set their total money equal to each other:
$100 + ($5 per day × d days) = $75 + ($7 per day × d days)
To solve for d, we can simplify this equation:
100 + 5d = 75 + 7d
Now, let's solve for d:
2d = 25
d = 12.5
Since days cannot be a fraction, we round 12.5 to the nearest whole number, which is 13. So, it will take them 13 days to have the same amount of money saved.
After 13 days, we can substitute the value of d into the equations to find out how much money they have each:
Judy's total money = $100 + ($5 per day × 13 days)
Judy's total money = $100 + $65
Judy's total money = $165
Elenore's total money = $75 + ($7 per day × 13 days)
Elenore's total money = $75 + $91
Elenore's total money = $166
Therefore, after 13 days, Judy will have $165 and Elenore will have $166.
To find the equations representing the total amount of money Judy and Elenore will have after saving for "d" days, we can use the given information.
1. Equation for Judy's savings after "d" days:
Judy starts with $100 and saves $5 per day. So, to find her total savings after "d" days, we can use the equation:
Total savings of Judy = Initial amount + (Rate of saving * Number of days)
= $100 + ($5 * d)
The equation representing Judy's savings after "d" days is:
Judy's savings = $100 + $5d
2. Equation for Elenore's savings after "d" days:
Elenore starts with $75 and saves $7 per day. So, her total savings after "d" days can be calculated using:
Total savings of Elenore = Initial amount + (Rate of saving * Number of days)
= $75 + ($7 * d)
The equation representing Elenore's savings after "d" days is:
Elenore's savings = $75 + $7d
3. Equation for finding the number of days required for Judy and Elenore to have the same amount:
To find the number of days it will take for Judy and Elenore to have the same amount of money saved, we can set their total savings equations equal to each other:
$100 + $5d = $75 + $7d
Now, we can solve this equation to find the value of "d" when they have the same amount saved.
4. After finding the number of days it took for Judy and Elenore to have the same amount saved, we can substitute this value of "d" into either Judy's or Elenore's savings equation to calculate the amount of money they each have.