Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day. (4 points)
Would the equation "5d + 100 = 7d + 75" 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?
Yes, the equation "5d + 100 = 7d + 75" can be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved. By solving the equation, you can determine the value of 'd', which represents the number of days it will take for them to reach the same savings.
To solve the equation, we can start by subtracting 5d from both sides of the equation: 100 = 7d - 5d + 75.
This simplifies to: 100 = 2d + 75.
Subtracting 75 from both sides: 25 = 2d.
Dividing by 2: d = 12.5.
Therefore, it will take them 12.5 days or approximately 13 days to have the same amount of money saved.
To calculate how much money they each have after this time, we can substitute the value of 'd' into either of the original equations.
For Judy, the amount saved after 13 days would be 5 * 13 + 100 = $165.
For Elenore, the amount saved after 13 days would be 7 * 13 + 75 = $166.
Therefore, Judy would have $165 saved and Elenore would have $166 saved after 13 days.
Yes, the equation "5d + 100 = 7d + 75" can be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved.
To solve this equation, you need to equate the savings of both Judy and Elenore. Here's how:
5d + 100 = 7d + 75
Subtracting 5d from both sides:
100 = 2d + 75
Then, subtracting 75 from both sides:
25 = 2d
Finally, dividing both sides by 2:
d = 12.5
So it will take approximately 12.5 days for Judy and Elenore to have the same amount of money saved. Since you cannot have half a day, we can round up to the nearest whole number, so it will take 13 days.
To find out how much money they have each after 13 days, we can substitute d = 13 into either Judy's or Elenore's savings equation. Let's use Judy's equation:
Judy's savings after 13 days = 5 * 13 + 100
= 65 + 100
= 165
Elenore's savings after 13 days = 7 * 13 + 75
= 91 + 75
= 166
Therefore, after 13 days, Judy will have $165 saved and Elenore will have $166 saved.
Yes, the equation "5d + 100 = 7d + 75" can be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved. In this equation, "d" represents the number of days.
To solve this equation, we can proceed as follows:
Step 1: Combine like terms
5d + 100 = 7d + 75
Step 2: Move all terms involving "d" to one side of the equation
5d - 7d = 75 - 100
-2d = -25
Step 3: Divide both sides of the equation by -2 to solve for "d"
d = (-25) / (-2)
d = 12.5
Thus, it will take approximately 12.5 days for Judy and Elenore to have the same amount of money saved.
After 12.5 days, Judy's savings can be calculated by substituting the value of "d" back into one of the original equations:
Judy's savings = 5d + 100
Judy's savings = 5 * 12.5 + 100
Judy's savings = 62.5 + 100
Judy's savings = $162.50
Similarly, Elenore's savings after 12.5 days can be calculated by substituting the value of "d" back into one of the original equations:
Elenore's savings = 7d + 75
Elenore's savings = 7 * 12.5 + 75
Elenore's savings = 87.5 + 75
Elenore's savings = $162.50
Therefore, after the number of days it took for both to have the same amount of money saved (12.5 days), Judy and Elenore will each have $162.50 saved.