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 same amount of money saved how much money they have each.
Let's say after the number of days Judy and Eleanor have the same amount of money saved, they both have x dollars.
The number of days it will take Judy to save x dollars is x/5
The number of days it will take Eleanor to save x dollars is x/7
The number of days it will take for both of them to have the same amount of money saved is LCM(x/5, x/7). We can find this by multiplying the highest power of each prime number that appears as a factor in either x/5 or x/7.
Since both x/5 and x/7 are already simplified, the LCM is 5 * 7 = 35.
After 35 days, both Judy and Eleanor will have saved the same amount of money, which is x = 35.
After 35 days, Judy will have saved 35 * 5 = $<<35*5=175>>175
After 35 days, Eleanor will have saved 35 * 7 = $<<35*7=245>>245.
Therefore, after 35 days, both Judy and Eleanor have $175 saved.
To find out how many days it took for Judy and Elenore to have the same amount of money saved, we need to set up an equation.
Let's assume it took them 'x' days to have the same amount of money saved.
Judy's savings after x days: 5 * x
Elenore's savings after x days: 7 * x
We can set up the equation:
100 + 5x = 75 + 7x
To solve for 'x', we need to isolate the variable on one side of the equation. Let's subtract 5x from both sides:
100 = 75 + 2x
Subtract 75 from both sides:
25 = 2x
Divide both sides by 2:
x = 12.5
Since 'x' represents the number of days, it cannot be a fractional value. We can round up the decimal value to the nearest whole number, which gives us 13 days.
Therefore, after 13 days, Judy and Elenore will have the same amount of money saved.
Judy's savings after 13 days: 5 * 13 = $65
Elenore's savings after 13 days: 7 * 13 = $91
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 denote the number of days it takes for them to have the same amount of money saved as "d".
Judy's money saved after "d" days can be expressed as: 100 + 5d
Elenore's money saved after "d" days can be expressed as: 75 + 7d
To find the value of "d" when both amounts are equal, we set up the equation:
100 + 5d = 75 + 7d
Subtracting 5d and 75 from both sides, we get:
25 = 2d
Dividing both sides by 2, we find:
d = 12.5
Since the number of days cannot be a decimal, we can round it up to the nearest whole number. So, it takes approximately 13 days for Judy and Elenore to have the same amount of money saved.
To find out how much money they each have after 13 days, we substitute "d" with 13 in the expressions for their money saved:
Judy's money saved = 100 + 5(13) = 100 + 65 = $165
Elenore's money saved = 75 + 7(13) = 75 + 91 = $166
So, after approximately 13 days, Judy will have $165 saved and Elenore will have $166 saved.