Solving an Investment ProblemThomas Flanagan has $40,000 to invest. He will put part of the money in an account
paying 4% interest and the remainder into stocks paying 6% interest. The total annual
income from these investments should be $2040. How much should he invest at each
rate?
Step 1 Readthe problem again. We must find the two amounts.
Step 2 Assign a variable.
Let ;
The formula for interest is Here the time tis 1 yr. Use a table to
organize the given information.
I=prt.
40,000-x= the amount to invest at 6%.
x=the amount to invest at 4%
EXAMPLE 6
72 CHAPTER 2 Linear Equations, Inequalities, and Applications
NOW TRYNOW TRY
EXERCISE 6
Gary Jones received a
$20,000 inheritance from his
grandfather. He invested some
of the money in an account
earning 3% annual interest
and the remaining amount in
an account earning 2.5% an-
nual interest. If the total an-
nual interest earned is $575,
how much is invested at each
rate?
NOW TRY ANSWER
- $15,000 at 3%; $5000 at 2.5%
Rate (as
Principal a decimal) Interest
x 0.04 0.04x
0.06
40,000 204040,000-x 0.06 1 40,000-x 2Multiply principal,
rate, and time (here,
1 yr) to get interest.
TotalStep 3 Write an equation.The last column of the table gives the equation.
interest at 4% interest at 6% total interest0.04x 2040
Step 4 Solvethe equation.
Distributive property.
Multiply.
Combine like terms.
Subtract 2400.
Divide byStep 5 State the answer.Thomas should invest $18,000 of the money at 4%. At
6%, he should invest
.
Step 6 Check.Find the annual interest at each rate. The sum of these two amounts
should total $2040.
and
$720+ $1320= $2040, as required.
0.04 1 $18,000 2 = $720 0.06 1 $22,000 2 = $1320
$40,000-$18,000=$22,000
x=18,000 -0.02.
- 0.02x=- 360
- 0.02x+ 2400 = 2040
0.04x+ 2400 - 0.06x= 2040
0.04x+0.06 1 40,000 2 - 0.06x= 2040
+ 0.06 1 40,000-x 2 =
+ =