Sam invests $6000 in treasury notes and bonds. The notes pay 8% annual interest and the bonds pay 10% annual interest. If the annual interest is $550, how much is invested in bonds?

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Answer 1 · 2016-08-21T22:46:38

$3500 in bonds.

8% = multiply by 0.08

10% = multiply by 0.10

Let $x$ $x$ be amount in notes and $y$ $y$ be amount in bonds.

$x + y = 6000$ $x + y = 6000$

$0.08 x + 0.10 y = 550$ $0.08x+0.10y = 550$

Multiply the second equation by 10:

$0.8 x + y = 5500 \Rightarrow y = 5500 - 0.8 x$ $0.8x + y = 5500 implies y = 5500 - 0.8x$

Substitute in for $y$ $y$ in the first equation:

$x + (5500 - 0.8 x) = 6000$ $x+ (5500 - 0.8x) = 6000$

$0.2 x = 500$ $0.2x = 500$

Multiply both sides by 5:

$x = 2500$ $x = 2500$

$\Rightarrow y = 3500$ $implies y = 3500$