Let's call the amount of money invested in bonds and stocks

b

and

s,

respectively. We know that the sum of these amounts should equal

$ 10000 .

With this information, we can write the following equation.

b + s = 10000

We also know that the bonds pay an annual interest of

3 %

while the stocks pay

5 % .

If we multiply these percentages in decimal form with their respective investments and add the products, its sum should equal

430 .

0.03 b + 0.05 s = 430

If we combine these equations we get a system of equations which we can solve with the Substitution Method.

{b + s = 10000 0.03 b + 0.05 s = 430 (I) (II)

$(I):$ $LHS - s = RHS - s$

{b = 10000 - s 0.03 b + 0.05 s = 430

$(II):$ $b = 10000 - s$

{b = 10000 - s 0.03 (10000 - s) + 0.05 s = 430

▼

(II):

Solve for

s

$(II):$ Distribute $0.03$

{b = 10000 - s 300 - 0.03 s + 0.05 s = 430

$(II):$ Add terms

{b = 10000 - s 300 + 0.02 s = 430

$(II):$ $LHS - 300 = RHS - 300$

{b = 10000 - s 0.02 s = 130

$(II):$ $LHS / 0.02 = RHS / 0.02$

{b = 10000 - s s = 6500

$(I):$ $s = 6500$

{b = 10000 - 6500 s = 6500

$(I):$ Subtract term

{b = 3500 s = 6500

He invested

$ 3500

in bonds and

$ 6500

in stocks.

Exercise 47 Page 603

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