Answer: Let's use a system of equations to solve this problem. We'll represent William's savings as W, Aiden's savings as A, and Daniel's savings as D.
We're given three pieces of information:
The sum of William and Aiden's savings is $1489:
W + A = 1489
The sum of William and Daniel's savings is $1688:
W + D = 1688
The ratio of Aiden to Daniel's savings is 3:4:
A/D = 3/4
Now, we can solve this system of equations. We'll start by finding the values of A and D using the third piece of information (the ratio):
A/D = 3/4
This implies that A = (3/4)D.
Now, we can substitute this expression for A into the first equation:
W + (3/4)D = 1489
Next, we'll substitute the expression for A into the second equation:
W + D = 1688
Now, we have a system of two equations with two variables:
W + (3/4)D = 1489
W + D = 1688
To solve this system, you can subtract the second equation from the first equation to eliminate W:
(W + (3/4)D) - (W + D) = 1489 - 1688
Simplify:
(3/4)D - D = -199
Now, combine the terms with D:
(3/4 - 1)D = -199
(3/4 - 4/4)D = -199
(-1/4)D = -199
Now, solve for D by multiplying both sides by -4:
D = -199 * (-4/1)
D = 796
So, Daniel's savings are $796. Now, we can find Aiden's savings using the ratio A/D = 3/4:
A = (3/4)D
A = (3/4) * 796
A = 597
Now that we know Aiden's and Daniel's savings, we can find William's savings by using the first equation:
W + A = 1489
W + 597 = 1489
Subtract 597 from both sides to find W:
W = 1489 - 597
W = 892
William has saved $892.