SOLUTION: Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested $4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested $4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest.       Log On


   

Question 147355: Hi, I dont know what Im doing wrong I need help please. Here is the question: One year ago you invested $4300 into three accounts that earn 3.25%, 4%, and 5.75% annual interest. The interest you earned after one year is $193. You remembered you invested three times as much in the 4% account than you did the 3.25% account. How much did you invest in each type of account? This is what i have so far, I dont think its right.
x + y + Z = 4300
325x + 400Y + 575z = 19300
Y=3x
x + (3x) + Z = 4300
4x + z = 4300
325x + 400 (3x) + z =19300
1525x +575z = 19300
(-575) 4x + z = 4300 (-575)
-2300x - 575z =-2472500
1525x + 575z = 19300
-775x = -2453200
x=3165.4 then when I do 3 times x to get y it doesnt fit with the total of 4300. I dont know please help me thank you.
Found 2 solutions by vleith, checkley77:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
x + w + y = 4300
0.0325x + 0.04w + 0.0575y = 193
3.25x + 4(3x) + 05.75y = 19300
4x + y = 4300
15.25x + 5.75y = 19300
Using substitution:
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

4%2Ax%2B1%2Ay=4300
15.25%2Ax%2B5.75%2Ay=19300

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

1%2Ay=4300-4%2AxSubtract 4%2Ax from both sides

y=%284300-4%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=4300-4%2Ax Now we've fully isolated y

Since y equals 4300-4%2Ax we can substitute the expression 4300-4%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


15.25%2Ax%2B5.75%2Ahighlight%28%284300-4%2Ax%29%29=19300 Replace y with 4300-4%2Ax. Since this eliminates y, we can now solve for x.

15.25%2Ax%2B5.75%2A%284300%29%2B5.75%28-4%29x=19300 Distribute 5.75 to 4300-4%2Ax

15.25%2Ax%2B24725-23%2Ax=19300 Multiply



15.25%2Ax%2B24725-23%2Ax=19300 Reduce any fractions

15.25%2Ax-23%2Ax=19300-24725 Subtract 24725 from both sides


15.25%2Ax-23%2Ax=-5425 Combine the terms on the right side



-7.75%2Ax=-5425 Now combine the terms on the left side.


cross%28%281%2F-7.75%29%28-7.75%2F1%29%29x=%28-5425%2F1%29%281%2F-7.75%29 Multiply both sides by 1%2F-7.75. This will cancel out -7.75%2F1 and isolate x

So when we multiply -5425%2F1 and 1%2F-7.75 (and simplify) we get



x=700 <---------------------------------One answer

Now that we know that x=700, lets substitute that in for x to solve for y

15.25%28700%29%2B5.75%2Ay=19300 Plug in x=700 into the 2nd equation

10675%2B5.75%2Ay=19300 Multiply

5.75%2Ay=19300-10675Subtract 10675 from both sides

5.75%2Ay=8625 Combine the terms on the right side

cross%28%281%2F5.75%29%285.75%29%29%2Ay=%288625%2F1%29%281%2F5.75%29 Multiply both sides by 1%2F5.75. This will cancel out 5.75 on the left side.

y=8625%2F5.75 Multiply the terms on the right side


y=1500 Reduce


So this is the other answer


y=1500<---------------------------------Other answer


So our solution is

x=700 and y=1500

which can also look like

(700,1500)

Notice if we graph the equations (if you need help with graphing, check out this solver)

4%2Ax%2B1%2Ay=4300
15.25%2Ax%2B5.75%2Ay=19300

we get


graph of 4%2Ax%2B1%2Ay=4300 (red) and 15.25%2Ax%2B5.75%2Ay=19300 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (700,1500). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (700,1500) into the system of equations


Let x=700 and y=1500. Now plug those values into the equation 4%2Ax%2B1%2Ay=4300

4%2A%28700%29%2B1%2A%281500%29=4300 Plug in x=700 and y=1500


2800%2B1500=4300 Multiply


4300=4300 Add


4300=4300 Reduce. Since this equation is true the solution works.


So the solution (700,1500) satisfies 4%2Ax%2B1%2Ay=4300



Let x=700 and y=1500. Now plug those values into the equation 15.25%2Ax%2B5.75%2Ay=19300

15.25%2A%28700%29%2B5.75%2A%281500%29=19300 Plug in x=700 and y=1500


10675%2B8625=19300 Multiply


19300=19300 Add


19300=19300 Reduce. Since this equation is true the solution works.


So the solution (700,1500) satisfies 15.25%2Ax%2B5.75%2Ay=19300


Since the solution (700,1500) satisfies the system of equations


4%2Ax%2B1%2Ay=4300
15.25%2Ax%2B5.75%2Ay=19300


this verifies our answer.




So x = $700
w = 3x = $2100
y = $1500
Verify your answers. Does 0.0325(700 + 0.04(2100) + 0.057(1500) = 193?


Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x+y+z=4300 (multiply by -.0575 & subtract. You neglected to change the % to decimals.)
.0325x+.04y+.0575z=193
-.0575x-.0575y-.0575z=-247.25
--------------------------------
-.0255x-.0175y=-54.25
y=3x
-.0255x-.0175*3x=-54.25
-.0255x-.0525x=-54.25
-.078x=-54.75
x=-54.25/-.078
x=695.52 amount invested @ 3.25%
3*695.52=2,086.54 amount invested @ 4%
695.52+2,086.54+y=4,300
y=4,300-695.52-2,086.54
y=1,517.94 amount invested @ 5.75%
proof:
.0325*695.52+.04*2,086.54+.0575*1,517.94=193
22.60+83.46+87.28=193
193~193