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?
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Judy's equation: Total money = $100 + $5 * d
Elenore's equation: 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, you need to set their equations equal to each other and solve for d:
$100 + $5 * d = $75 + $7 * d
After finding the value of d, you can substitute it back into either Judy's or Elenore's equation to find out how much money they have each.
The equation representing how much money Judy will have in total after saving for d days is:
Total amount = $100 + ($5 * d)
The equation representing how much money Elenore will have in total after saving for d days is:
Total amount = $75 + ($7 * d)
The equation 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)
To solve this equation, we can subtract $5d from both sides:
$100 = $75 + $2d
Next, subtract $75 from both sides:
$25 = $2d
Finally, divide both sides by $2:
d = 12.5
Since we cannot have half a day, we can round up to the nearest whole number, so it would take approximately 13 days for Judy and Elenore to have the same amount of money saved.
After 13 days, Judy would have $100 + ($5 * 13) = $165, and Elenore would have $75 + ($7 * 13) = $164.
To calculate how much money Judy will have in total after saving for d days, we can use the equation:
Judy's total amount = Judy's initial amount + (Judy's saving per day * number of days)
= $100 + ($5 * d)
= $100 + 5d
So, the equation representing how much money Judy will have in total after saving for d days is: Judy's total amount = $100 + 5d.
Similarly, to calculate how much money Elenore will have in total after saving for d days, we can use the equation:
Elenore's total amount = Elenore's initial amount + (Elenore's saving per day * number of days)
= $75 + ($7 * d)
= $75 + 7d
So, the equation representing how much money Elenore will have in total after saving for d days is: Elenore's total amount = $75 + 7d.
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 amounts equal to each other and solve for d:
Judy's total amount = Elenore's total amount
$100 + 5d = $75 + 7d
Simplifying the equation, we get:
2d = 25
d = 12.5
So, 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 both to have the same amount of money saved, we can substitute this value back into either of the equations to find out how much money they each have.
Using Judy's equation:
Judy's total amount = $100 + 5d
= $100 + 5 * 12.5
= $100 + 62.5
= $162.5
Using Elenore's equation:
Elenore's total amount = $75 + 7d
= $75 + 7 * 12.5
= $75 + 87.5
= $162.5
So, after the number of days it took for Judy and Elenore to have the same amount of money saved, they each have $162.5.