Math 60
3.4: Motion, Money, and Mixture Problems
Elementary Algebra
Linear Motion Word Problems
1.
Motion Two cars leave the same town at the same time. The northbound car is traveling 9 miles per hour less
than the southbound car. After 3 hours the cars are 375 miles apart. Find the speed of the northbound car.
Let x = ___________________________________________________________________
North
Town
North
South
2.
Rate 


South
Time
= Distance
=
=
Motion A hummingbird flying at 53 miles per hour is to overtake a pigeon flying at 24 miles per hour which
started 20 minutes earlier. How long will it take the hummingbird to overtake the pigeon? Round your answer to
the nearest hundredth.
Let t = ___________________________________________________________________
Hummingbird
Pigeon
Hummingbird
Pigeon
Rate 


3.4: Motion, Money, and Mixture Problems – Math 60
Time
= Distance
=
=
Page 1 of 9
3.
Motion John and Cindy are walking to the Cerritos Mall, each traveling the same route. Cindy is traveling at 3
miles per hour and John is traveling at 5 miles per hour. In how many hours will they be 7.5 miles apart?
Let t = ___________________________________________________________________
John
Cindy
4.
Rate 


Time
= Distance
=
=
Motion Mark is in training for a triathlon. Each morning Mark travels a total of 50 miles by biking for 1 ½ hours
and then running for 45 minutes. If Mark runs at a speed of 8 miles per hour, how fast does he bike? Round your
answer to the nearest tenth.
Let x = ___________________________________________________________________
Bike
Run
Rate 


3.4: Motion, Money, and Mixture Problems – Math 60
Time
= Distance
=
=
Page 2 of 9
Linear Liquid Mixture Word Problems
5.
Liquid Mixture How many liters of 18% salt solution must be added to 92 liters of a 61% salt solution to get a
41% salt solution?
Let x = the number of liters of the 18% salt solution
Solution 1
(18% guy)
Liters of Solution
+
Solution 2
(61% guy)
=
+
=
+
=
Mixture
(41% guy)
% Salt
Liters of Salt
6.
Liquid Mixture A chemist has a 16% Hydrochloric Acid (HCL) solution and a 30% HCL solution. An order is
placed for a 25% HCL solution. How much of the 16% and 30% HCL solutions must be mixed together to yield
20 ounces of 25% HCL solution. Round you answer to the nearest hundredth of an ounce.
Let x = ___________________________________________________________________
Solution 1
(16% guy)
Ounces of Solution
+
Solution 2
(30% guy)
=
+
=
+
=
Mixture
(25% guy)
% HCL
Ounces of HCL
3.4: Motion, Money, and Mixture Problems – Math 60
Page 3 of 9
7.
Liquid Mixture Sydney is experimenting by mixing alcoholic liqueurs in a large pitcher for her 16th birthday
party. Sydney opens her parent’s liquor cabinet and finds Bailey’s Irish Cream and Jose Cuervo Especial Tequila.
She reads the label and finds that Bailey’s is 17% alcohol by volume and Jose Cuervo is 40% alcohol by volume.
She mixes 5 cups of Jose Cuervo with 1 cup of Bailey’s, tastes the drink, and says “yuck!”, then pours it down the
sink. What is the percent of alcohol in her mixture? Round your answer to the nearest tenth of a percent.
Let x = ___________________________________________________________________
Bailey’s
(17% guy)
Cups of Liqueur
+
Jose Cuervo
(40% guy)
=
+
=
+
=
Mixture
(??? % guy)
% Alcohol
Cups of Alcohol
8.
Liquid Mixture Sydney’s brother Troy sees what she has done. When Sydney leaves the room, he sneaks in and
removes the Jose Cuervo bottle, noting that the 750 milliliter bottle is exactly one–quarter full. He decides to
pour enough pure water into the bottle until the bottle is full to the top. What is the percent of alcohol in this
diluted tequila solution? (Recall that the Jose Cuervo Especial Tequila was 40% alcohol by volume.)
Let x = ___________________________________________________________________
Jose Cuervo
(40% guy)
mL of Liquid
+
Pure Water
(0% guy)
=
+
=
+
=
Diluted Mixture
(??? % guy)
% Alcohol
mL of Alcohol
3.4: Motion, Money, and Mixture Problems – Math 60
Page 4 of 9
Linear Solid Mixture Word Problems
9.
Solid Mixture A 10–pound mixture of trail mix sells for $2.20 per pound. If raisins cost $2.45 per pound, and
peanuts cost $2.10 per pound, how many pounds of each are used? Round your answer to the nearest tenth.
Let x = ___________________________________________________________________
Item 1
+
Raisins @ $2.45
Pounds of Item
Item 2
=
Peanuts @ $2.10
+
=
+
=
Mixture
Trail Mix @ $2.20
Price per pound
Total Cost of Item
10.
Solid Mixture How many pounds of chocolate Bon-Bons selling for $2.40 per pound should be mixed with 3
pounds of caramels selling for $1.20 a pound to obtain a candy mixture selling for $2.04 per pound?
Let x = ___________________________________________________________________
Item 1
+
Bon-Bons @ $2.40
Pounds of Item
Item 2
=
Caramels @ $1.20
+
=
+
=
Mixture
Candy Mix @ $2.04
Price per pound
Total Cost of Item
3.4: Motion, Money, and Mixture Problems – Math 60
Page 5 of 9
Linear Two Items/Two Prices/Total Value Word Problems
11.
Employment Rosemary works two part-time jobs while attending Cerritos College. During the day she works at
the Cerritos College Bookstore and earns $8.25 per hour. In the evening she delivers pizzas for Papa John’s pizza
earning $9.25 per hour. If Rosemary earned $247 last week from working a total of 28 hours, find how many
hours Rosemary worked at Papa John’s last week.
Let x = ___________________________________________________________________
Bookstore
Hours Worked
+
+
Papa John’s
=
=
Total
Hourly Wage
+
Total Earned
12.
=
Buying Tickets Sergio wants to buy his wife tickets to see Wicked at the Pantages Theater on Valentine’s Day.
Sergio goes online and finds that the matinee show has sold out of all 120 available tickets costing $65.75 each;
while the evening show is still has tickets available. If a total of 300 tickets were sold for Valentine’s Day and the
Pantages Theater took in $25,080 in ticket sales, what was the cost of each ticket for the evening show?
Let x = ___________________________________________________________________
Matinee
Number of Tickets
+
+
Evening
=
=
Total
Price Per Ticket
Total Cost of Tickets
3.4: Motion, Money, and Mixture Problems – Math 60
+
=
Page 6 of 9
Linear Simple Interest Word Problems (I = p  r  t)
13.
Simple Interest George invested $19,000 for one year, part at 11% simple interest and part at 12% simple
interest. If the annual interest income from the two investments was $2,200, how much was invested at each rate?
Let x = the amount of money invested at 11% simple interest
George
$19,000
Interest Rate
Money Invested
Interest Earned
11%
$x
(x)(0.11)(1) =
0.11x
12%
$ (19,000 – x)
(19,000 – x)(0.12)(1) =
0.12(19,000 – x)
Interest Earned + Interest Earned  Total Interest
@ 11%
@ 12%
0.11x  0.12 19, 000  x   2, 200
14.
Simple Interest Cindy receives an annual interest income of $1,740. She has some money invested at 6% and
$4,000 less than that amount invested at 9%? Find the amount of money Cindy has invested at each rate.
Let x = ___________________________________________________________________
Cindy
$ ????
Interest Rate
Money Invested
Interest Earned
6%
$x
(x)(0.06)(1) =
0.06x
9%
$ (x – 4,000)
(x – 4,000)(0.09)(1) =
0.09(x – 4,000)
Interest Earned + Interest Earned  Total Interest
@ 6%
3.4: Motion, Money, and Mixture Problems – Math 60
@ 9%
Page 7 of 9
15.
Simple Interest Natalie has some money invested at 3 ¼ % simple interest and $750 less than that amount
invested at 4% simple interest. If the annual interest income from both accounts is the same, find the total amount
of Natalie’s investment.
Let x = ___________________________________________________________________
Natalie
$ ????
Interest Rate
Money Invested
3¼%
4%
Interest Earned
Interest 1Earned = Interest Earned
@ 34 %
16.
@ 4%
Simple Interest David invested $8,000, part at 5% simple interest and part at 6% simple interest for a period of 1
year. How much was invested in each account if the interest earned in the 5% account was $12.50 less than the
interest earned in the 6% account?
Let x = ___________________________________________________________________
David
$8,000
Interest Rate
Money Invested
Interest Earned
Interest Earned = Interest Earned 12.50
@ 5%
3.4: Motion, Money, and Mixture Problems – Math 60
@ 6%
Page 8 of 9
Answers to Section 3.4 – Motion, Money, and Mixture Problems
#
Algebraic Equation
Algebraic Solution
Answer to the Question
1.
3  x  9   3x  375
x = 67
Northbound Car: 58 mph
2.
53t  24  t  13 
t = 0.275862…
Hummingbird: 0.28 hours
t = 3.75
3.75 hours
x  29.333333…
Bike: 29.3 mph
3.
4.
3
2
5t  3t  7.5
x  34 8  50
5.
0.18x  0.61 92   0.41 x  92 
x = 80
80 L of 18% salt
6.
0.16 x  0.30  20  x   0.25  20 
x  7.142857…
7.
0.17 1  0.40  5  6x
7.14 oz of 16% HCL
12.86 oz. of 30% HCL
x  0.361666…
36.2% alcohol
8.
0.40 187.5  0  562.5  750x
x = 0.1
10% alcohol
9.
2.45x  2.10 10  x   2.20 10 
x  2.857142…
10.
2.40 x  1.20  3  2.04  x  3
Raisins: 2.9 pounds
Peanuts: 7.1 pounds
x=7
Bon-Bons: 7 pounds
11.
8.25  28  x   9.25x  247
x = 16
Papa John’s: 16 hours
12.
120  65.75  180 x  25,080
x = 95.50
Evening Ticket: $95.50
13.
0.11x  0.12 19,000  x   2, 200
x = 8,000
14.
0.06 x  0.09  x  4,000   1,740
x = 14,000
15.
0.0325x  0.04  x  750 
x = 4,000
Total Investment: $7,250
16.
0.05x  0.06 8,000  x   12.50
x = 4,250
$4,250 @ 5%
$3,750 @ 6%
3.4: Motion, Money, and Mixture Problems – Math 60
$8,000 @ 11%
$11,000 @ 12%
$14,000 at 6%
$10,000 at 9%
Page 9 of 9