Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day
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/day) * 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/day) * 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 savings equal to each other and solve for d:
$100 + ($5/day) * d = $75 + ($7/day) * d
4) After the number of days it took for both Judy and Elenore to have the same amount of money saved, their total savings would be:
Total savings = $100 + ($5/day) * d = $75 + ($7/day) * d
We would need the value of d from the previous equation to substitute into this equation to find the exact total savings for each person.
To determine the equations and answer the questions, we need to consider the given information:
Judy starts with $100 and saves $5 per day.
Elenore starts with $75 and saves $7 per day.
1. Equation for Judy's total savings after d days:
Total savings = Initial amount + (savings per day × number of days)
= $100 + ($5 × d)
= $100 + 5d
2. Equation for Elenore's total savings after d days:
Total savings = Initial amount + (savings per day × number of days)
= $75 + ($7 × d)
= $75 + 7d
3. Equation to find the number of days it takes for Judy and Elenore to have the same amount of money saved:
$100 + 5d = $75 + 7d
Start with the same initial amount and add the savings for each person until they equalize. Here, we equate their total savings after d days:
4. Solving the equation for d:
Subtracting 5d from both sides to isolate the variable on one side:
$100 = $75 + 2d
Then subtracting $75 from both sides:
$25 = 2d
Finally, dividing both sides by 2:
d = 12.5
So it would take approximately 12.5 days for Judy and Elenore to have the same amount of money saved.
5. After the number of days it took for them to have the same amount saved:
Substituting the value of d (12.5) into either equation, let's use Judy's equation:
Total savings = $100 + ($5 × 12.5)
= $100 + $62.5
= $162.5
Therefore, both Judy and Elenore would have $162.5 each after approximately 12.5 days.
To answer these questions, we need to break it down step by step:
1. Equation for Judy's savings: Judy saves $5 per day, so after saving for d days, she will have saved a total of $5*d. Therefore, 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. Equation for Elenore's savings: Elenore saves $7 per day, so after saving for d days, she will have saved a total of $7*d. Therefore, 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. Equation for finding the number of days it takes for Judy and Elenore to have the same amount of money saved: To find the number of days it will take for them to have the same amount of money saved, we need to set their total money equations equal to each other. So, we can write an equation like this: $100 + $5*d = $75 + $7*d.
4. After finding the number of days it takes for Judy and Elenore to have the same amount of money saved, we can substitute that value back into either Judy's or Elenore's total money equation to find out how much money they each have. For example, if we determine that it takes 20 days, we can substitute d = 20 into one of the total money equations. Let's use Judy's equation: Judy's Total Money = $100 + $5*20 = $100 + $100 = $200. Therefore, after 20 days, Judy has $200. We can then use the same method to find out how much money Elenore has after 20 days by substituting d = 20 into her total money equation: Elenore's Total Money = $75 + $7*20 = $75 + $140 = $215. So, after 20 days, Elenore has $215.