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?
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.
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.
Let's break down the equation:
- "5d" represents the amount of money that Judy saves in "d" days (since she saves $5 per day).
- "7d" represents the amount of money that Elenore saves in "d" days (since she saves $7 per day).
- "100" represents the initial amount of money Judy has ($100).
- "75" represents the initial amount of money Elenore has ($75).
The equation is formed by equating the total amount saved by Judy to the total amount saved by Elenore. Since both Judy and Elenore have the same amount of money saved at the end, their savings plus their initial amount of money should be equal.
Simplifying the equation:
5d + 100 = 7d + 75
To solve this equation, you need to isolate the variable "d" on one side. Here's how you can do it step by step:
1. Start by subtracting 5d from both sides of the equation:
100 = 7d - 5d + 75
2. Simplify the equation:
100 = 2d + 75
3. Next, subtract 75 from both sides:
100 - 75 = 2d
4. Simplify further:
25 = 2d
5. Finally, divide both sides by 2 to solve for "d":
d = 25 / 2
d = 12.5
Therefore, by solving the equation, we find that it will take 12.5 days for Judy and Elenore to have the same amount of money saved.