Applications of Linear Equation

APPLICATIONS OF LINEAR EQUATION IN ONE

VARIABLE

Specific ObjectivesAt the end of the lesson the students are expected to:• Translate word statement into algebraic expressions• Solve word problems involving linear equation in one variable such as:

a. Number Problems

b. Geometric Problems

Specific Objectivesc. Money and Coin Problems

d. Investment Problems

e. Age Problems

f. Mixture Problems

g. Uniform Motion Problems

h. Work Problems

i. Clock Problems

Translating Word Statement Into Algebraic Expression

Illustrative Examples:1. Three more than x.2. Six decreased by a.3. The product of 5 and b.4. The quotient of x and y.5. Two more than twice s.6. The sum of seven and d.7. The difference of t and 4.

Translating Word Statement Into Algebraic Expression

Illustrative Examples:8. The square of the hypotenuse (h).9. The cube of the side (s).10. The square root of 5.11. The quantity two less than m.12. Eleven multiplied by the quantity x plus five.13. Ten increased by seven equals seventeen.

Translating Word Statement Into Algebraic Expression

Illustrative Examples:14. a is equal to the difference of x and five.15. The product of two number is 85 and one number is five.16. A number (n) increased by five gives twelve.17. Fifteen more than six equals n.

Translating Word Statement Into Algebraic Expression

Illustrative Examples:18. The area (A) of a rectangle equals the length (L) times the width (W).19. The length (L) of a rectangle is 21 inches greater than the width (W).20. Mario was x years old four years ago. Represent his age six years from now.

Number ProblemsSample Problems:1. (No. 13 / Page 110) Find a number such that 10 less than 2/3 the number is ¼ the number.2. (No. 14 / 110) Find a positive number such that ten times the number is 16 more than twice the number.3. (No. 15 /110) Five two consecutive even integers such that 4 times the smaller is two more than 3 times the larger number.

Number ProblemsSample Problems:4. If a number is divided by 4, and the quotient is increased by 8, the result is 16. Find the number. 5. The sum of three numbers is 99. The first is twice the second and the third is three times the first. Find the three numbers.

Geometric ProblemsSample Problems:1. (No.18 / 110) Find the dimensions of a rectangle whose length is one foot longer than twice its width and whose perimeter is 20 feet.2. The perimeter of a rectangle is 68m. The length of the rectangle is 2m more than the width. Find the length of the rectangle.

Geometric ProblemsSample Problems:3. (No. 17 / 110) Find the perimeter of a triangle if one side is 11 inches, another side is 1/3 the perimeter, and the third side is one less than ¼ the perimeter.

Money and Coins ProblemsSample Problems:1. Katrina has 84 bills consisting of P10 and P50. If the total amount of her money is P3280, how many pieces of each kind of bill does she have?2. (No. 2 / 110) The original price of a pair of binoculars is $74. The sale price is $51.80. How much was the markdown?

Investment ProblemsSample Problems:1. A businessman invested Php 16,000 part at 9% and the rest at 4% annual interest. How much does he invest at 4%, if his annual income from both investments is Php 990?

Investment ProblemsSample Problems:2. (No. 28 / 111) You inherit $13,000 and you decide to invest in two different investments: one paying 10% and the other 14%. A year later, your investments are worth $14,580. How much did you originally invest in each account?

Age ProblemsSample Problems:1. A father is 30 years old and his son is 5 years old. In how many years will the father be twice as old as the son?2. Lina is one-sixth as old as her sister. In twelve years, she will be only one-third as old. Find their present ages.

Age ProblemsSample Problems:3. Five years ago, Mike was twice as old as Berto. The sum of their ages six years hence will be forty years. What is the present age of each?

Mixture ProblemsSample Problems:1. How many liters of 70% acid solution should be added to a 250 liter solution which contains25% acid so that the resulting mixture will be 40% acid?2. A 40-gram alloy containing 35% gold is to be melted with 20 gram of alloy containing 50% gold. How much percentage of gold is the resulting alloy?

Uniform Motion ProblemsTime = 0 Time = t speed (rate) = v

S

S = vt

Uniform Motion ProblemsAirplane Travelling With the Wind: Speed of Airplane = x Wind Speed = y

Resultant Speed = x + y

Uniform Motion ProblemsAirplane Travelling Against the Wind: Speed of Airplane = x Wind Speed = y

Resultant Speed = x - y

Uniform Motion ProblemsBoat Travelling Downstream:

Boat Speed = x

Resultant Speed = x + y

Stream Speed = y

Uniform Motion ProblemsBoat Travelling Upstream:

Boat Speed = x

Resultant Speed = x - y

Stream Speed = y

Uniform Motion ProblemsSample Problems:1. On a trip Harry drove a steady speed for 3 hours. An accident slowed his speed by 30 mph for the last part of the trip. If the 190-mile trip took 4 hours, what was his speed during the first part of the trip?

Uniform Motion ProblemsSample Problems:2. (No. 45 / 112) College roommates leave for their first class in the same building. One walks at 2 mph and the other rides his bike at a slow 6 mph pace. How long will it take each get to class if the walker takes 12 minutes longer to get to class and they travel at the same path?

Uniform Motion ProblemsSample Problems:3. A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far downstream should he go if he is to return in 7/4 hrs after leaving?4. A boat takes 2/3 as much time to travel downstream from C to D as to return. If the rate of the river’s current is 8 kph, what is the speed of the boat in still water?

Work ProblemsThe formula for “Work” Problems that involve two persons is

This formula can be extended for more than two persons. It can also be used in problems that involve pipes filling up a tank.

Work ProblemsSample Problems:

1. Suppose Carlo and Judd can do the project together in 4 days. If Carlo can finish the project alone in 6 days, how long will it take Judd to do the project if he works alone?

Work ProblemsSample Problems:

2. (No. 49 / 112) Tracey and Robin deliver Coke products to local convenient store. Tracey can complete the deliveries in 4 hour alone. Robin can do it in 6 hours alone. If they decide to work together on a Saturday, how long will it take?

Digit ProblemsSample Problems:

1. The ten’s digit of a number is three times the one’s digit. The sum of the digits in the number is 8. What is the number?

2. The tens digit of a two digit number is 3 more than the one’s digit. The number is 8 more than six times the sum of the digits. find the number?

Clock ProblemsSample Problems:

1. How many minutes after 3:00 PM will the minute hand of the clock overtakes the hour hand?

2. At what time after 12:00 noon will the hour hand and the minute hand form an angle of 120 degrees?

Clock Problems