Ryan saved $55 more than Jim. Chris saved 6 times as much as Jim. Donna saved half as much as Chris. If the children saved $3245 altogether how much did each child save?
R = J + 55
C = 6 J
C = 2 D
R + J + C + D = 3245
Four equations; four unknowns.
J + 55 + J + 2D + D = 3245
2J + 3D = 3190
C/3 + (3/2) C = 3190
(11/6)C = 3190
C = 1740
J = 290
D = 870
R = 345
To solve this problem, we will use a system of equations based on the given information.
Let's assume that Jim saved x dollars.
Then Ryan saved $55 more than Jim, so Ryan saved x + $55.
Chris saved 6 times as much as Jim, so Chris saved 6x dollars.
Donna saved half as much as Chris, so Donna saved (1/2) * 6x = 3x dollars.
According to the problem, the total amount saved by all the children is $3245, so we can set up the equation:
x + (x + $55) + 6x + 3x = $3245
Now we can combine like terms:
11x + $55 = $3245
Next, we need to isolate the variable x by subtracting $55 from both sides:
11x = $3245 - $55
11x = $3190
Now we can solve for x by dividing both sides by 11:
x = $3190 / 11
x ≈ $290
So Jim saved approximately $290.
To find how much each child saved, we substitute this value of x back into our equations:
Jim saved x = $290
Ryan saved x + $55 = $290 + $55 = $345
Chris saved 6x = 6 * $290 = $1740
Donna saved 3x = 3 * $290 = $870
Therefore, each child saved:
Jim: $290
Ryan: $345
Chris: $1740
Donna: $870