Step 3 Write an equation.Multiply amount by rate to get the interest earned.
Interest interest total
at 6% plus at 7% is interest.0.06x 790
Step 4 Solve. Distributive property
Multiply by 100.
Multiply.
Combine like terms.
Subtract 14,000.
Divide by 13.Step 5 State the answer.She should invest $5000 at 6% and
$7000 at 7%.
Step 6 Check.Investing $5000 at 6% and $7000 at 7% gives total interest of
, as required.
NOW TRYOBJECTIVE 4 Solve problems involving denominations of money.
0.06 1 $5000 2 +0.07 1 $7000 2 =$300+ $490=$790
$5000+$2000=
x= 5000
13 x= 65,000
13 x+14,000= 79,000
6 x+ 7 x+14,000= 79,000
6 x+ 7 x+ 7120002 = 79,000
0.06x+ 0.07x+0.07 120002 = 790
+ 0.07 1 x+ 20002 =
142 CHAPTER 2 Linear Equations and Inequalities in One Variable
Number of Bills Denomination Total Value
x 10 10 x
x+ 25 551 x+ 252To get the total value in problems that involve different denominations of
money or items with different monetary values, we multiply.
Money Denominations Problems
number value of one item total value
For example, 30 dimes have a monetary value of. Fifteen $5 bills
have a value of 151 $5 2 =$75.A table is also helpful for these problems.
301 $0.10 2 = $3
:
PROBLEM-SOLVING HINT
Solving a Money Denominations ProblemA bank teller has 25 more $5 bills than $10 bills. The total value of the money is
$200. How many of each denomination of bill does she have?
Step 1 Readthe problem. We must find the number of each denomination of bill.
Step 2 Assign a variable.
Let
Then x+ 25 =the number of $5 bills.
x=the number of $10 bills.
EXAMPLE 4
Organize the given
information in a table.NOW TRY
EXERCISE 3
A financial advisor invests
some money in a municipal
bond paying 3% annual
interest and $5000 more than
that amount in a certificate
of deposit paying 4% annual
interest. To earn $410 per
year in interest, how much
should he invest at each rate?
NOW TRY ANSWER
3.$3000 at 3%; $8000 at 4%
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