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?___
1) The equation that represents how much money Judy will have in total after saving for d days is:
Judy's total savings = $100 + $5*d
2) The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total savings = $75 + $7*d
3) The equation that would be 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
4) After the number of days it took for both to have the same amount of money saved, the total savings for both will be:
$100 + $5*d = $75 + $7*d
Simplifying, we get:
$25 = $2*d
Dividing both sides by 2, we get:
d = 12.5
Therefore, after 12.5 days, both Judy and Elenore will have the same amount of money saved.
Judy will have $100 + $5*12.5 = $162.50
Elenore will have $75 + $7*12.5 = $162.50.
The equation that represents how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + $5 * d
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + $7 * d
To find out how many days it will take for Judy and Elenore to have the same amount of money saved, we can set their total money equal to each other:
$100 + $5 * d = $75 + $7 * d
After the number of days it took both to have the same amount of money saved, they would each have:
Total money = $100 + $5 * d (the same amount for both Judy and Elenore)
To answer these questions, we need to understand the relationship between the amount of money saved and the number of days.
1. To find out how much money Judy will have in total after saving for d days, we can use the equation:
Judy's total money = Initial amount + (Savings per day * Number of days)
Judy's total money = $100 + ($5 * d)
So, the equation representing how much money Judy will have in total after saving for d days is: Judy's total money = $100 + ($5 * d)
2. To find out how much money Elenore will have in total after saving for d days, we can use the equation:
Elenore's total money = Initial amount + (Savings per day * Number of days)
Elenore's total money = $75 + ($7 * d)
So, the equation representing how much money Elenore will have in total after saving for d days is: Elenore's total money = $75 + ($7 * d)
3. 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 equations equal to each other and solve for d:
Judy's total money = Elenore's total money
$100 + ($5 * d) = $75 + ($7 * d)
Simplifying the equation, we get:
$100 - $75 = ($7 * d) - ($5 * d)
$25 = $2 * d
Dividing both sides by $2, we get:
d = $25 / $2
So, the equation to find out how many days it will take for Judy and Elenore to have the same amount of money saved is: d = ($25 / $2) or simply d = 12.5 (rounded to the nearest whole number).
4. After 12 days (rounded to the nearest whole number), Judy and Elenore will have the same amount of money saved. To find out how much money they will each have, substitute the value of d (12) into their respective total money equations:
Judy's total money = $100 + ($5 * 12) = $100 + $60 = $160
Elenore's total money = $75 + ($7 * 12) = $75 + $84 = $159
So, after 12 days, Judy will have $160 and Elenore will have $159.