Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
After the number of days it took both to have the same amount of money saved, how much money do they have each?
Judy needs to save $100 - $75 = $<<100-75=25>>25 more to have the same amount as Elenore.
So, Judy would save for $25 รท $5/day = <<25/5=5>>5 days.
In 5 days of saving, Judy saved $5/day x 5 days = $<<5*5=25>>25.
So, they both have a total of $75 + $25 = $<<75+25=100>>100 each. Answer: \boxed{100}.
To determine the number of days it took for Judy and Elenore to have the same amount of money, we can set up an equation.
Let's assume it took them 'x' number of days.
Judy's money = $100 + ($5/day) * x
Elenore's money = $75 + ($7/day) * x
To find 'x', we'll set Judy's money equal to Elenore's money and solve for 'x':
$100 + ($5/day) * x = $75 + ($7/day) * x
Subtracting $75 from both sides:
$100 - $75 = ($7/day) * x - ($5/day) * x
Simplifying:
$25 = ($2/day) * x
Dividing both sides by $2/day:
$25 / ($2/day) = x
x = 12.5 days
Since we cannot have half a day, we can round it up to 13 days.
To find out how much money they each have after 13 days, we substitute 'x' back into our equations:
Judy's money = $100 + ($5/day) * 13 = $100 + $65 = $165
Elenore's money = $75 + ($7/day) * 13 = $75 + $91 = $166
Therefore, after 13 days, Judy has $165 and Elenore has $166 saved.
To find out how many days it takes for Judy and Elenore to have the same amount of money saved, we need to set up an equation.
Let's assume it takes "x" days for both of them to have the same amount of money saved.
In "x" days, Judy will have saved 5 * x dollars, and Elenore will have saved 7 * x dollars.
According to the given information, Judy starts with $100 and Elenore starts with $75.
So, the equation becomes:
100 + 5x = 75 + 7x
To solve this equation, let's isolate the variables. Subtracting 5x from both sides gives:
100 = 75 + 2x
Subtracting 75 from both sides gives:
25 = 2x
Finally, dividing both sides by 2 gives:
x = 12.5
Therefore, it will take 12.5 days for Judy and Elenore to have the same amount of money saved.
Now, let's calculate how much money they have each after 12.5 days.
Judy saves $5 per day, so after 12.5 days, she will have saved 5 * 12.5 = $62.5.
Elenore saves $7 per day, so after 12.5 days, she will have saved 7 * 12.5 = $87.5.
Hence, after 12.5 days, Judy will have $62.5 and Elenore will have $87.5.