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?
Let x be the number of days that have passed.
Judy has saved 5x dollars.
Elenore has saved 7x dollars.
After the number of days it took both to have the same amount of money saved, they will have 5x + 75 = 7x + 100.
Subtracting 5x from both sides of the equation, we get 75 = 2x + 100
Subtracting 100 from both sides of the equation, we get -25 = 2x
Dividing both sides of the equation by 2, we get x = -12.5
We disregard the negative value because days cannot be negative.
After 12.5 days, Judy has saved 5 * 12.5 = <<5*12.5=62.5>>62.5 dollars.
After 12.5 days, Elenore has saved 7 * 12.5 = <<7*12.5=87.5>>87.5 dollars. Answer: \boxed{62.5, 87.5}.
To find out how many days it will take for Judy and Elenore to have the same amount of money saved, we can set up an equation.
Let the number of days be represented by 'x'.
Judy's savings after x days = $100 + ($5 * x)
Elenore's savings after x days = $75 + ($7 * x)
To find when they have the same amount of money saved, we need to find when their savings are equal, so we can set up the equation:
100 + 5x = 75 + 7x
Now, we can solve for 'x'.
Subtracting 5x from both sides:
100 = 75 + 2x
Subtracting 75 from both sides:
25 = 2x
Dividing both sides by 2:
x = 12.5
Since we cannot have half a day, we can round this up to the nearest whole number, which is 13.
This means it will take 13 days for Judy and Elenore to have the same amount of money saved.
Now, let's calculate how much money they each have after 13 days.
Judy's savings after 13 days = $100 + ($5 * 13)
Judy's savings after 13 days = $100 + $65
Judy's savings after 13 days = $165
Elenore's savings after 13 days = $75 + ($7 * 13)
Elenore's savings after 13 days = $75 + $91
Elenore's savings after 13 days = $166
Therefore, after 13 days, Judy will have $165 saved and Elenore will have $166 saved.
To find out how many days it will take for both Judy and Elenore to have the same amount of money saved, we need to set up an equation.
Let's assume it takes 'n' days for them to have the same amount of money saved.
Judy's savings after 'n' days can be calculated by multiplying the amount she saves per day by the number of days: $5 * n = $5n
Elenore's savings after 'n' days can be calculated by multiplying the amount she saves per day by the number of days: $7 * n = $7n
To find the point at which they have the same amount of money, we need to find when these two equations are equal:
$5n = $7n
Now we can solve for 'n':
Subtract $5n from both sides: $7n - $5n = $2n
Simplify: $2n = 0
Divide both sides by $2: n = 0
It seems that there was an error in the equation, as the solution is not possible. Let's check the given information again:
Judy has $100 and is saving $5 per day. The equation for Judy's savings is $5n = $100.
Elenore has $75 and is saving $7 per day. The equation for Elenore's savings is $7n = $75.
Now, let's solve for 'n' again:
For Judy: $5n = $100
Divide both sides by $5: n = $100 / $5
Simplify: n = 20
For Elenore: $7n = $75
Divide both sides by $7: n = $75 / $7
Simplify: n ≈ 10.71
Since 'n' represents the number of days, we can't have a fractional number of days. Therefore, we round it up to the nearest whole number to ensure at least 10 days have passed.
Thus, after 11 days, Judy will have $100 + ($5 * 11) = $155, and Elenore will have $75 + ($7 * 11) = $152.
So, after 11 days, Judy will have $155 and Elenore will have $152.