Adrian has $12,000 invested in a savings account which pays 5%, a time deposit paying 7% and a bond that pays 10%. He has $1000 less invested in the bond than in his savings account, and he earned $860 in annual interest. How much money is in each account?
What is your equation ?
a+b+c=12000
.5a+.7b(1000-b)+.10c=860
makes no sense,
I think you just wrote something down because I asked you for an equation.
you have 3 variables in your first equation, so you will need 3 different equations to solve
if a, b, and c are you different investments, then
a+b+c = 860 , not 1000. Where did it say that the total was 1000
"Adrian has $12,000 invested in a savings account which pays 5%"
---> first investment is 12,000, at 5% interest that would come to $600
"a time deposit paying 7% " , assuming that is the savings account
----> 2nd investment is x , at 7% interest will yield .07x
"He has $1000 less invested in the bond than in his savings account"
---- 3rd investment is x-1000 , at 10% will yield
.1(x-1000)
now what will be your equation ?
.5(12000)+.07x+.1(x-1000)=12000
close, 2 errors!
5% = .05, not .5
why do you set the total to 1200, didn't it say 860 ?
make the change, now solve that equation.
To solve this problem, we will set up a system of equations. Let's start by assigning variables to the unknown values:
Let:
Amount invested in the savings account = S
Amount invested in the time deposit = T
Amount invested in the bond = B
Given-
1. Adrian has $12,000 invested in a savings account, which pays 5%.
2. Adrian has $1000 less invested in the bond than in his savings account.
3. The total annual interest earned is $860.
Equation 1: S + T + B = $12,000 (Total amount invested)
Equation 2: B = S - $1000 (The bond investment is $1000 less than the savings account investment)
Equation 3: 0.05S + 0.07T + 0.10B = $860 (Interest earned from each investment at their respective rates)
Now, let's solve the system of equations to find the values of S, T, and B.
Substituting Equation 2 into Equation 1:
S + T + (S - $1000) = $12,000
2S + T = $13,000 --- Equation 4
Substituting Equation 2 into Equation 3:
0.05S + 0.07T + 0.10(S - $1000) = $860
0.05S + 0.07T + 0.10S - $100 = $860
0.15S + 0.07T = $960 --- Equation 5
Using Equations 4 and 5, we can solve for S and T. Let's solve them simultaneously:
Multiply Equation 4 by 15 to eliminate decimals:
30S + 15T = $195,000 --- Equation 6
Multiply Equation 5 by 2 to eliminate decimals:
0.30S + 0.14T = $1,920 --- Equation 7
Subtract Equation 7 from Equation 6:
(30S + 15T) - (0.30S + 0.14T) = $195,000 - $1,920
29.70S + 14.86T = $193,080
Divide both sides by 0.02 to simplify:
S + 0.50T = $6,520 --- Equation 8
Now we have a system of two equations (Equations 8 and 4) with two variables (S and T). Let's solve it:
1.) Multiply Equation 8 by 2:
2S + T = $13,040 --- Equation 9
2.) Subtract Equation 9 from Equation 4:
(2S + T) - (2S + T) = $13,040 - $13,000
0 = $40
The equation yields 0 = $40, which is not possible. It indicates that there is no solution to the system of equations. Double-checking the problem's conditions may be necessary.