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. The equation to find out how many days it will take for Jane and Ellis to have the same amount of money saved is: \[ 100 + 5d = 75 + 7d \]

D. After solving the equation from part C for d, you would find how much each will have saved at that time.

First, solve for d: \[ 100 + 5d = 75 + 7d \] \[ 100 - 75 = 7d - 5d \] \[ 25 = 2d \] \[ d = 12.5 \]

Now, substitute \( d = 12.5 \) back into either equation to find the amount they will have saved:

For Jane: \[ J(12.5) = 100 + 5(12.5) = 100 + 62.5 = 162.5 \]

For Ellis: \[ E(12.5) = 75 + 7(12.5) = 75 + 87.5 = 162.5 \]

Thus, after 12.5 days, Jane and Ellis each will have saved: \[ 162.5 \]