Jane has $100 and Ellis has $75. Jane is saving $5 per day and Ellis is saving $7 per day. (4 points)

Question

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A. What equation represents how much money Jane will have in total after saving for d days? Response area

B. What equation represents how much money Ellis will have in total after saving for d days? Response area

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? Response area

D. After the amount of time found above, how much will Jane and Ellis each have saved? Response area

Answer 1

A. The equation that represents how much money Jane will have in total after saving for \( d \) days is:
\[ J(d) = 100 + 5d \]

B. The equation that represents how much money Ellis will have in total after saving for \( d \) days is:
\[ E(d) = 75 + 7d \]

C. To find out how many days it will take for Jane and Ellis to have the same amount of money saved, set their equations equal to each other:
\[ 100 + 5d = 75 + 7d \]

D. After solving the equation from part C to find \( d \), we can substitute that value back into either equation to find how much they will have saved. After solving, we find \( d = 25 \). To find how much Jane and Ellis will each have saved, we substitute \( d = 25 \):
\[ J(25) = 100 + 5(25) = 100 + 125 = 225 \]
\[ E(25) = 75 + 7(25) = 75 + 175 = 250 \]

So, after 25 days, Jane will have $225 and Ellis will have $250.