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EXAMPLE 3.33
Stacey has $20,000 to invest in two different bank accounts. One account pays interest at 3% per year and the other
account pays interest at 5% per year. How much should she invest in each account if she wants to earn 4.5% interest per
year on the total amount?
Solution
We will fill in a chart to organize our information. We will use the simple interest formula to find the interest earned in
the different accounts.
The interest on the mixed investment will come from adding the interest from the account earning 3% and the interest
from the account earning 5% to get the total interest on the $20,000.
The amount invested is the principal for each account.
We enter the interest rate for each account.
We multiply the amount invested times the rate to get the interest.
Notice that the total amount invested, 20,000, is the sum of the amount invested at 3% and the amount invested at 5%.
And the total interest, is the sum of the interest earned in the 3% account and the interest earned in the
5% account.
As with the other mixture applications, the last column in the table gives us the equation to solve.
Write the equation from the interest earned.
Solve the equation.
amount invested at 3%
Find the amount invested at 5%.
Check.
Stacey should invest $5,000 in the account that
earns 3% and $15,000 in the account that earns 5%.
3.3 • Solve Mixture Applications 331
TRY IT 3.65 Remy has $14,000 to invest in two mutual funds. One fund pays interest at 4% per year and the
other fund pays interest at 7% per year. How much should she invest in each fund if she wants
to earn 6.1% interest on the total amount?
TRY IT 3.66 Marco has $8,000 to save for his daughter’s college education. He wants to divide it between
one account that pays 3.2% interest per year and another account that pays 8% interest per
year. How much should he invest in each account if he wants the interest on the total
investment to be 6.5%?
SECTION 3.3 EXERCISES
Practice Makes Perfect
Solve Coin Word Problems
In the following exercises, solve each coin word problem.
161. Jaime has $2.60 in dimes
and nickels. The number
of dimes is 14 more than
the number of nickels.
How many of each coin
does he have?
162. Lee has $1.75 in dimes
and nickels. The number
of nickels is 11 more than
the number of dimes.
How many of each coin
does he have?
163. Ngo has a collection of
dimes and quarters with a
total value of $3.50. The
number of dimes is seven
more than the number of
quarters. How many of
each coin does he have?
164. Connor has a collection of
dimes and quarters with a
total value of $6.30. The
number of dimes is 14
more than the number of
quarters. How many of
each coin does he have?
165. A cash box of $1 and $5
bills is worth $45. The
number of $1 bills is three
more than the number of
$5 bills. How many of
each bill does it contain?
166. Joe’s wallet contains $1
and $5 bills worth $47.
The number of $1 bills is
five more than the
number of $5 bills. How
many of each bill does he
have?
167. Rachelle has $6.30 in
nickels and quarters in
her coin purse. The
number of nickels is twice
the number of quarters.
How many coins of each
type does she have?
168. Deloise has $1.20 in
pennies and nickels in a
jar on her desk. The
number of pennies is
three times the number
of nickels. How many
coins of each type does
she have?
169. Harrison has $9.30 in his
coin collection, all in
pennies and dimes. The
number of dimes is three
times the number of
pennies. How many coins
of each type does he
have?
170. Ivan has $8.75 in nickels
and quarters in his desk
drawer. The number of
nickels is twice the
number of quarters. How
many coins of each type
does he have?
171. In a cash drawer there is
$125 in $5 and $10 bills.
The number of $10 bills is
twice the number of $5
bills. How many of each
are in the drawer?
172. John has $175 in $5 and
$10 bills in his drawer. The
number of $5 bills is three
times the number of $10
bills. How many of each
are in the drawer?
173. Carolyn has $2.55 in her
purse in nickels and
dimes. The number of
nickels is nine less than
three times the number
of dimes. Find the
number of each type of
coin.
174. Julio has $2.75 in his
pocket in nickels and
dimes. The number of
dimes is 10 less than
twice the number of
nickels. Find the number
of each type of coin.
175. Chi has $11.30 in dimes
and quarters. The
number of dimes is three
more than three times the
number of quarters. How
many of each are there?
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176. Tyler has $9.70 in dimes
and quarters. The
number of quarters is
eight more than four
times the number of
dimes. How many of each
coin does he have?
177. Mukul has $3.75 in
quarters, dimes and
nickels in his pocket. He
has five more dimes than
quarters and nine more
nickels than quarters.
How many of each coin
are in his pocket?
178. Vina has $4.70 in
quarters, dimes and
nickels in her purse. She
has eight more dimes
than quarters and six
more nickels than
quarters. How many of
each coin are in her
purse?
Solve Ticket and Stamp Word Problems
In the following exercises, solve each ticket or stamp word problem.
179. The school play sold $550
in tickets one night. The
number of $8 adult
tickets was 10 less than
twice the number of $5
child tickets. How many of
each ticket were sold?
180. If the number of $8 child
tickets is seventeen less
than three times the
number of $12 adult
tickets and the theater
took in $584, how many
of each ticket were sold?
181. The movie theater took in
$1,220 one Monday night.
The number of $7 child
tickets was ten more than
twice the number of $9
adult tickets. How many
of each were sold?
182. The ball game sold $1,340
in tickets one Saturday.
The number of $12 adult
tickets was 15 more than
twice the number of $5
child tickets. How many of
each were sold?
183. The ice rink sold 95 tickets
for the afternoon skating
session, for a total of
$828. General admission
tickets cost $10 each and
youth tickets cost $8
each. How many general
admission tickets and
how many youth tickets
were sold?
184. For the 7:30 show time,
140 movie tickets were
sold. Receipts from the
$13 adult tickets and the
$10 senior tickets totaled
$1,664. How many adult
tickets and how many
senior tickets were sold?
185. The box office sold 360
tickets to a concert at the
college. The total receipts
were $4170. General
admission tickets cost $15
and student tickets cost
$10. How many of each
kind of ticket was sold?
186. Last Saturday, the
museum box office sold
281 tickets for a total of
$3954. Adult tickets cost
$15 and student tickets
cost $12. How many of
each kind of ticket was
sold?
187. Julie went to the post
office and bought both
$0.41 stamps and $0.26
postcards. She spent
$51.40. The number of
stamps was 20 more than
twice the number of
postcards. How many of
each did she buy?
188. Jason went to the post
office and bought both
$0.41 stamps and $0.26
postcards and spent
$10.28. The number of
stamps was four more
than twice the number of
postcards. How many of
each did he buy?
189. Maria spent $12.50 at the
post office. She bought
three times as many
$0.41 stamps as $0.02
stamps. How many of
each did she buy?
190. Hector spent $33.20 at
the post office. He bought
four times as many $0.41
stamps as $0.02 stamps.
How many of each did he
buy?
191. Hilda has $210 worth of
$10 and $12 stock shares.
The numbers of $10
shares is five more than
twice the number of $12
shares. How many of each
does she have?
192. Mario invested $475 in
$45 and $25 stock shares.
The number of $25 shares
was five less than three
times the number of $45
shares. How many of each
type of share did he buy?
3.3 • Solve Mixture Applications 333
Solve Mixture Word Problems
In the following exercises, solve each mixture word problem.
193. Lauren in making 15 liters
of mimosas for a brunch
banquet. Orange juice
costs her $1.50 per liter
and champagne costs her
$12 per liter. How many
liters of orange juice and
how many liters of
champagne shouldshe
use for the mimosas to
cost Lauren $5 per liter?
194. Macario is making 12
pounds of nut mixture
with macadamia nuts and
almonds. Macadamia
nuts cost $9 per pound
and almonds cost $5.25
per pound. How many
pounds of macadamia
nuts and how many
pounds of almonds
should Macario use for
the mixture to cost $6.50
per pound to make?
195. Kaapo is mixing Kona
beans and Maui beans to
make 25 pounds of coffee
blend. Kona beans cost
Kaapo $15 per pound and
Maui beans cost $24 per
pound. How many
pounds of each coffee
bean should Kaapo use
for his blend to cost him
$17.70 per pound?
196. Estelle is making 30
pounds of fruit salad from
strawberries and
blueberries. Strawberries
cost $1.80 per pound and
blueberries cost $4.50 per
pound. If Estelle wants
the fruit salad to cost her
$2.52 per pound, how
many pounds of each
berry should she use?
197. Carmen wants to tile the
floor of his house. He will
need 1000 square feet of
tile. He will do most of the
floor with a tile that costs
$1.50 per square foot, but
also wants to use an
accent tile that costs
$9.00 per square foot.
How many square feet of
each tile should he plan
to use if he wants the
overall cost to be $3 per
square foot?
198. Riley is planning to plant a
lawn in his yard. He will
need nine pounds of
grass seed. He wants to
mix Bermuda seed that
costs $4.80 per pound
with Fescue seed that
costs $3.50 per pound.
How much of each seed
should he buy so that the
overall cost will be $4.02
per pound?
199. Vartan was paid $25,000
for a cell phone app that
he wrote and wants to
invest it to save for his
son’s education. He wants
to put some of the money
into a bond that pays 4%
annual interest and the
rest into stocks that pay
9% annual interest. If he
wants to earn 7.4%
annual interest on the
total amount, how much
money should he invest in
each account?
200. Vern sold his 1964 Ford
Mustang for $55,000 and
wants to invest the
money to earn him 5.8%
interest per year. He will
put some of the money
into Fund A that earns 3%
per year and the rest in
Fund B that earns 10%
per year. How much
should he invest into each
fund if he wants to earn
5.8% interest per year on
the total amount?
201. Stephanie inherited
$40,000. She wants to put
some of the money in a
certificate of deposit that
pays 2.1% interest per
year and the rest in a
mutual fund account that
pays 6.5% per year. How
much should she invest in
each account if she wants
to earn 5.4% interest per
year on the total amount?
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202. Avery and Caden have
saved $27,000 towards a
down payment on a
house. They want to keep
some of the money in a
bank account that pays
2.4% annual interest and
the rest in a stock fund
that pays 7.2% annual
interest. How much
should they put into each
account so that they earn
6% interest per year?
203. Dominic pays 7% interest
on his $15,000 college
loan and 12% interest on
his $11,000 car loan. What
average interest rate does
he pay on the total
$26,000 he owes? (Round
your answer to the
nearest tenth of a
percent.)
204. Liam borrowed a total of
$35,000 to pay for
college. He pays his
parents 3% interest on
the $8,000 he borrowed
from them and pays the
bank 6.8% on the rest.
What average interest
rate does he pay on the
total $35,000? (Round
your answer to the
nearest tenth of a
percent.)
Everyday Math
205. As the treasurer of her daughter’s Girl Scout
troop, Laney collected money for some girls and
adults to go to a 3-day camp. Each girl paid $75
and each adult paid $30. The total amount of
money collected for camp was $765. If the
number of girls is three times the number of
adults, how many girls and how many adults
paid for camp?
206. Laurie was completing the treasurer’s report for
her son’s Boy Scout troop at the end of the
school year. She didn’t remember how many
boys had paid the $15 full-year registration fee
and how many had paid the $10 partial-year fee.
She knew that the number of boys who paid for
a full-year was ten more than the number who
paid for a partial-year. If $250 was collected for
all the registrations, how many boys had paid the
full-year fee and how many had paid the partial-
year fee?
Writing Exercises
207. Suppose you have six quarters, nine dimes, and
four pennies. Explain how you find the total
value of all the coins.
208. Do you find it helpful to use a table when solving
coin problems? Why or why not?
209. In the table used to solve coin problems, one
column is labeled “number” and another column
is labeled “value.” What is the difference between
the “number” and the “value?”
210. What similarities and differences did you see
between solving the coin problems and the ticket
and stamp problems?
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
3.3 • Solve Mixture Applications 335