SOLUTION: James has a certain amount of money invested at 5% annual interest and $500 more than twice that amount invested in bonds yielding 7%. His total annual income from interest is $187
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Question 1152475: James has a certain amount of money invested at 5% annual interest and $500 more than twice that amount invested in bonds yielding 7%. His total annual income from interest is $187. How much does he have invested at each rate? Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! x equals the amount of money he has invested at 5%.
2x + 500 equals the amount of money he has invested at 7%.
.05x + .07 * (2x + 500) = 187
simplify to get:
.05x + .14x + 35 = 187
combine like terms and subtract 35 from both sides of the equation to get:
.19x = 152
solve for x to get:
x = 800
2x + 500 = 2100
.05 * 800 + .07 * 2100 = 187
this confirms the value for x is good.
your solution is:
he has 800 invested at 5% and 2100 invested at 7%.
Let x be the amount invested at 5%.
Then the amount invested at 7% is (2x+500) dollars.
The partial interests are 0.05x dollars and 0.07*(2x+500) dollars.
The equation for the total interest is
0.05x + 0.07*(2x+500) = 187 dollars.
From the equation
x = = 800.
ANSWER. $800 were invested at 5%, and 2*800+500 = 2100 dollars were invested at 7%.
CHECK. 0.05*800 + 0.07*2100 = 187 dollars. ! Precisely correct !
Solved.
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It is a standard and typical problem on investments.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
