Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day. (4 points)%0D%0AWhat equation represent how much money Judy will have in total after saving for d days? %0D%0A%0D%0AWhat equation represents how much money Elenore will have in total after saving for d days? %0D%0A %0D%0A%0D%0AWhat 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? %0D%0A%0D%0AAfter 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 representing how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + ($5 per day x d days)
2) The equation representing how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + ($7 per day x d days)
3) The equation to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's total money = Elenore's total money
($100 + ($5 per day x d days)) = ($75 + ($7 per day x d days))
4) After the number of days it took for both to have the same amount of money saved, they will both have that amount of money.
To calculate the total amount of money Judy will have after saving for d days, we can use the equation:
Judy's total money = Judy's initial money + (Judy's saving per day × number of days)
The equation will be: J = $100 + ($5 × d)
To calculate the total amount of money Elenore will have after saving for d days, we can use the equation:
Elenore's total money = Elenore's initial money + (Elenore's saving per day × number of days)
The equation will be: E = $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 and solve the equation.
Judy's total money = Elenore's total money
Thus, we have the equation: $100 + ($5 × d) = $75 + ($7 × d)
To find out the amount of money they each have after the number of days it takes for them to have the same amount of money saved, we can substitute the value of d into either Judy's or Elenore's total money equation.
To find the equation for how much money Judy will have in total after saving for d days, we can use the formula:
Judy's Total Money = Judy's initial money + (Judy's saving per day * number of days)
Judy's Total Money = $100 + ($5 * d)
Judy's Total Money = $100 + 5d
Now, let's find the equation for how much money Elenore will have in total after saving for d days using a similar approach:
Elenore's Total Money = Elenore's initial money + (Elenore's saving per day * number of days)
Elenore's Total Money = $75 + ($7 * d)
Elenore's Total Money = $75 + 7d
To determine 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:
Judy's Total Money = Elenore's Total Money
$100 + 5d = $75 + 7d
Now, let's solve this equation to find the number of days it will take:
100 + 5d = 75 + 7d
Subtract 5d from both sides:
100 = 75 + 2d
Subtract 75 from both sides:
25 = 2d
Divide both sides by 2:
d = 12.5
Therefore, it will take approximately 12.5 days for Judy and Elenore to have the same amount of money saved.
After the number of days it took for them to have the same amount of money saved, we can substitute the value of d into either Judy or Elenore's total money equation to find out how much they have saved.
Using Judy's equation:
Judy's Total Money = $100 + ($5 * 12.5)
Judy's Total Money = $100 + $62.5
Judy's Total Money = $162.5
Using Elenore's equation:
Elenore's Total Money = $75 + ($7 * 12.5)
Elenore's Total Money = $75 + $87.5
Elenore's Total Money = $162.5
Therefore, after 12.5 days, both Judy and Elenore will have $162.5 saved.