Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day.
After 1 day, Judy will have $100 + $5 = $<<100+5=105>>105
After 1 day, Elenore will have $75 + $7 = $<<75+7=82>>82
After 2 days, Judy will have $105 + $5 = $<<105+5=110>>110
After 2 days, Elenore will have $82 + $7 = $<<82+7=89>>89
After 3 days, Judy will have $110 + $5 = $<<110+5=115>>115
After 3 days, Elenore will have $89 + $7 = $<<89+7=96>>96
After 4 days, Judy will have $115 + $5 = $<<115+5=120>>120
After 4 days, Elenore will have $96 + $7 = $<<96+7=103>>103
After 5 days, Judy will have $120 + $5 = $<<120+5=125>>125
After 5 days, Elenore will have $103 + $7 = $<<103+7=110>>110
To find out when Judy will have more money than Elenore, we need to determine how many days it will take for Judy's savings to surpass Elenore's.
First, we need to calculate the difference between their savings per day:
Judy saves $5 per day
Elenore saves $7 per day
The difference is $7 - $5 = $2.
Next, we need to figure out how many days it will take for Judy's savings to exceed Elenore's, considering the difference in their savings per day.
Let's assume X is the number of days it will take. So, after X days, the difference in their savings will be $2X.
Judy will have saved $5X after X days.
Elenore will have saved $7X after X days.
For Judy to have more money than Elenore, we set up the inequality:
$100 + $5X > $75 + $7X
Now, we can solve for X:
$5X - $7X > $75 - $100
-$2X > -$25 (By subtracting $75 from both sides)
To solve for X, we need to divide both sides by -2, but to maintain the inequality, we need to flip its direction:
X < -$25 / -2
X < 12.5 (By dividing both sides by -2)
Since X represents the number of days, it cannot be a fraction. Therefore, we round down to the nearest whole number:
X < 12
Therefore, Judy will have more money than Elenore within 12 days.
To find out how long it will take for Judy and Elenore to have the same savings, we need to determine the difference in their savings amounts and divide it by the difference in their daily savings rates.
1. Calculate the difference in their savings amounts:
Judy's savings = $100
Elenore's savings = $75
Difference = $100 - $75 = $25
2. Calculate the difference in their daily savings rates:
Judy's daily savings = $5
Elenore's daily savings = $7
Difference = $7 - $5 = $2
3. Determine the number of days it will take for their savings to be the same:
Days = Difference in savings / Difference in daily savings rates
Days = $25 / $2 = 12.5
Based on the calculations, it will take approximately 12.5 days for Judy and Elenore to have the same savings. However, since we cannot have half a day, we can round up the answer to 13 days.