Let's break down each part of the problem step by step:
A. What equation represents how much money Jane will have in total after saving for d days?
Jane starts with $100 and saves $5 per day. Therefore, the equation for Jane’s total amount after d days is: \[ y = 5d + 100 \]
B. What equation represents how much money Ellis will have in total after saving for d days?
Ellis starts with $75 and saves $7 per day. Therefore, the equation for Ellis’s total amount after d days is: \[ y = 7d + 75 \]
C. What equation would be used to find out how many days it will take for Jane and Ellis to have the same amount of money saved?
To find the number of days (d) at which Jane and Ellis have the same total amount of money, we can set their equations equal to each other: \[ 5d + 100 = 7d + 75 \]
D. After the amount of time found above, how much will Jane and Ellis each have saved?
Let's solve for \(d\) from the equation \(5d + 100 = 7d + 75\):
- Rearranging gives: \[ 100 - 75 = 7d - 5d \] \[ 25 = 2d \] \[ d = 12.5 \]
Now, substitute \(d = 12.5\) into either Jane's or Ellis's equation to find out how much they each will have:
For Jane:
\[ y = 5(12.5) + 100 \] \[ y = 62.5 + 100 = 162.5 \]
For Ellis:
\[ y = 7(12.5) + 75 \] \[ y = 87.5 + 75 = 162.5 \]
Conclusion:
After 12.5 days, both Jane and Ellis will have $162.50.
To summarize:
A. \(y = 5d + 100\)
B. \(y = 7d + 75\)
C. \(5d + 100 = 7d + 75\)
D. After 12.5 days, both will have $162.50.
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