Jane has $50 and Ellis has $24. Jane is saving $4 per day and Ellis is saving $6 per day.
What equation represents how much money Jane will have in total after saving for d days? __________.
What equation represents how much money Ellis will have in total after saving for d days? ________.
What equation would be used to find out how many it will take for Jane and Ellis to have the same amount of money saved? ______.
After the amount of time found above, how much will Jane and Ellis each have saved? _____.
The robot tutor actually started off quite well, but then messed up
after d days, Jane will have 4d + 50 , (the robot had that)
after d days, Ellis will have 6d + 24 , the robot had that too
how long before the have the same ?
6d + 24 = 4d + 50 , the robot even had that, but then totally messed up ....
2d = 26
d = 13
so it will take 13 days for them to have the same, and that will
be 4(13) + 50 = 102
or, we could find Ellis' which must be the same ...
6(13) + 24 = 102
The equation to represent how much money Jane will have in total after saving for d days is:
Jane's total savings = $50 + ($4 × d)
The equation to represent how much money Ellis will have in total after saving for d days is:
Ellis' total savings = $24 + ($6 × d)
The equation to find out how many days it will take for Jane and Ellis to have the same amount of money saved is:
$50 + ($4 × d) = $24 + ($6 × d)
To solve this equation, you need to isolate the variable d:
($4 × d) - ($6 × d) = $24 - $50
-($2 × d) = -$26
Divide both sides by -2: d = 13
After 13 days, Jane and Ellis will each have saved:
Jane: $50 + ($4 × 13) = $50 + $52 = $102
Ellis: $24 + ($6 × 13) = $24 + $78 = $102
To find the equation that represents how much money Jane will have in total after saving for d days, we can use the formula: total money = initial amount + (saving rate * number of days).
In this case, Jane's initial amount is $50, and she saves $4 per day. Therefore, the equation representing Jane's total money after d days would be:
Jane's total money = $50 + ($4 * d)
Now, let's find the equation that represents how much money Ellis will have in total after saving for d days. Using the same formula, with an initial amount of $24 and a saving rate of $6 per day, the equation representing Ellis's total money after d days would be:
Ellis's total money = $24 + ($6 * d)
To determine how many days it will take for Jane and Ellis to have the same amount of money saved, we can set the two equations equal to each other and solve for d:
$50 + ($4 * d) = $24 + ($6 * d)
Simplifying the equation, we get:
$50 - $24 = ($6 * d) - ($4 * d)
$26 = $2 * d
Dividing both sides by 2, we find:
d = $26 / $2
d = 13
Therefore, it will take 13 days for Jane and Ellis to have the same amount of money saved.
Finally, to determine how much Jane and Ellis will each have saved after 13 days, we can substitute the value of d into their respective equations:
Jane's total money after 13 days = $50 + ($4 * 13) = $50 + $52 = $102
Ellis's total money after 13 days = $24 + ($6 * 13) = $24 + $78 = $102
Therefore, after 13 days, Jane and Ellis will each have $102 saved.
Jane: 50 + 4d
Ellis: 24 + 6d
4d + 50 = 6d + 24
Jane: (6d + 24) - 4d = 50 + 2d
Ellis: (6d + 24) - 6d = 24
Both: 50 + 2d