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, would they have 162.50 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.
To solve the equation, you would subtract 5d from both sides to isolate the variable:
100 = 7d - 5d + 75
Combine like terms:
100 = 2d + 75
Subtract 75 from both sides:
25 = 2d
Finally, divide 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.
As for whether they would have $162.50 each, let's calculate their savings after 12.5 days:
Judy's savings = $5 * 12.5 + $100 = $62.50 + $100 = $162.50
Elenore's savings = $7 * 12.5 + $75 = $87.50 + $75 = $162.50
Therefore, yes, after 12.5 days, Judy and Elenore would each have $162.50 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 the equation, we can start by simplifying both sides:
5d + 100 = 7d + 75
Subtracting 5d from both sides, we get:
100 = 2d + 75
Then, subtracting 75 from both sides, we have:
25 = 2d
Finally, dividing both sides by 2, we find:
d = 12.5
Therefore, it would take approximately 12.5 days for Judy and Elenore to have the same amount of money saved.
Regarding the second question, if they both save for this many days, they would not have $162.50 each. To calculate how much they would have, we can substitute the value of d back into one of the original savings equations.
For Judy:
5d + 100 = 5(12.5) + 100 = 62.50 + 100 = $162.50
For Elenore:
7d + 75 = 7(12.5) + 75 = 87.50 + 75 = $162.50
So, both Judy and Elenore would have $162.50 each after 12.5 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, we first need to simplify it:
5d + 100 = 7d + 75
We want to isolate the variable "d" on one side of the equation, so we'll start by subtracting 5d from both sides:
100 = 7d - 5d + 75
Simplifying further, we have:
100 = 2d + 75
Next, we'll subtract 75 from both sides to get all the variables on one side:
100 - 75 = 2d
25 = 2d
Now, we divide both sides by 2 to solve for d:
25/2 = d
So, d = 12.5 days.
Therefore, it will take 12.5 days for Judy and Elenore to have the same amount of money saved.
Now, to find out if they will have $162.50 each after this amount of time, we'll substitute d = 12.5 into the original equations for Judy and Elenore:
For Judy:
Amount saved = 5 * d + 100 = 5 * 12.5 + 100 = $162.50
For Elenore:
Amount saved = 7 * d + 75 = 7 * 12.5 + 75 = $162.50
So, after 12.5 days, both Judy and Elenore would indeed have $162.50 each saved.