Application of Linear Equations

Application of Linear Equations in One Variable

By: Chiradee Tagle

​Solving word problems involving linear equations in one variable

​

• Geometry - related problems

• Money - related problems​

​How do we solve a word problem?

​How do we solve a word problem?

​In solving word problems, we;

1) Choose a variable to represent the one unknown quantity and represent any other unknown quantities in terms of this variable.​

2) Draw a diagram if possible to visualize the known facts or summarize the information in a tabular form.​

3) Translate word problems into an equation.

4) Solve the equation.

5) Check the answer by substituting the result in the original equation.

​Recall: Let's try this!

​Recall: Let's try this!

I have a number, if you increase it by 3, multiply the sum by 5, and subtract 10 from the product, the result is 25. Guess my number.

Let x be the number.​

​Recall: Let's try this!

I have a number, if you increase it by 3, multiply the sum by 5, and subtract 10 from the product, the result is 25. Guess my number.

Let x be the number.​

5(x + 3) - 10 = 25

5x + 15 - 10 = 25

5x + 5 = 25

5x = 20

x = 4

The number is 4.​

Multiple Choice

Twice a number less than ten is fifty.

• 20

• -20

• 30

• -30

Multiple Choice

Ten more than four times the sum of a number and five is 70.

• 10

• 15

• 20

• 25

Multiple Choice

Lei is twice as old as Kaye. The sum of their ages is 72. How old is Lei?

• 24

• 31

• 45

• 48

Multiple Choice

Josh is 8 years older than his brother Ryan. The sum of their ages is 38, how old will Ryan be in twelve years?

• 15

• 23

• 27

• 35

Multiple Choice

Harry is now twice as old as Ron. Seven years ago, the sum of their ages was 16. How old is Ron now?

• 10

• 20

• 17

• 27

1) A 10-foot wood block is to be cut into two pieces so that the longer piece is 4 times the shorter. Find the length of each piece.

​

Let x be the length shorter piece, and

let 4x be the length of longer piece​

1) A 10-foot wood block is to be cut into two pieces so that the longer piece is 4 times the shorter. Find the length of each piece.

​

Let x be the length shorter piece, and

let 4x be the length of longer piece​

x + 4x = 10​

5x = 10

x = 2​

​

1) A 10-foot wood block is to be cut into two pieces so that the longer piece is 4 times the shorter. Find the length of each piece.

​

Let x be the length shorter piece, and

let 4x be the length of longer piece​

x + 4x = 10​

5x = 10

x = 2​

​

Therefore, ​the shorter piece of the board is 2 feet, and the longer piece of the board is 8 feet.

1) A 10-foot wood block is to be cut into two pieces so that the longer piece is 4 times the shorter. Find the length of each piece.

​

2) The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 meters more than twice its width. What are the length and the width of the pool?

​

Let y be the width of the pool, and

let 2y + 2 be the length of the pool

2) The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 meters more than twice its width. What are the length and the width of the pool?

​

Let y be the width of the pool, and

let 2y + 2 be the length of the pool

2(2y + 2) + 2y = 154​

4y + 4 + 2y = 154

6y + 4 = 154

6y = 150

y = 25​​

2) The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 meters more than twice its width. What are the length and the width of the pool?

​

Let y be the width of the pool, and

let 2y + 2 be the length of the pool

2(2y + 2) + 2y = 154​

4y + 4 + 2y = 154

6y + 4 = 154

6y = 150

y = 25​​

Therefore, ​the length and the width of the swimming pool are 52 meters and 25 meters respectively.

2) The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 meters more than twice its width. What are the length and the width of the pool?

​

3) Jenny buys a triangular pennant for souvenir. The base of the pennant is 35 centimeters shorter than the two other sides, which are equal. If the perimeter of the pennant is 145 centimeters, find its dimensions.

​

Let a be the measure of each equal side, and

let a - 35 be the measure of the base

3) Jenny buys a triangular pennant for souvenir. The base of the pennant is 35 centimeters shorter than the two other sides, which are equal. If the perimeter of the pennant is 145 centimeters, find its dimensions.

​

Let a be the measure of each equal side, and

let a - 35 be the measure of the base

a + a + (a - 35) = 145​

3a - 35 = 145

3a = 180

a = 60​

3) Jenny buys a triangular pennant for souvenir. The base of the pennant is 35 centimeters shorter than the two other sides, which are equal. If the perimeter of the pennant is 145 centimeters, find its dimensions.

​

Let a be the measure of each equal side, and

let a - 35 be the measure of the base

a + a + (a - 35) = 145​

3a - 35 = 145

3a = 180

a = 60​

Therefore, ​the base is 25 centimeters, and the other two sides is 60 centimeters each.

3) Jenny buys a triangular pennant for souvenir. The base of the pennant is 35 centimeters shorter than the two other sides, which are equal. If the perimeter of the pennant is 145 centimeters, find its dimensions.

​

Multiple Choice

Suppose a rectangle and an equilateral triangle have the same perimeter. The length of the rectangle is three times the width. Each side of the triangle is 8cm. Find the length and the width of the rectangle.

• length = 24cm

  width = 6cm

• length = 9cm

  width = 3cm

• length = 22cm

  width = 8cm

• length = 12cm

  width = 4cm

Multiple Choice

The second angle of a triangle is three times as large as the first. The third angle is 30° more than the first. Find the measure of each angle.

• $$30\degree,90\degree,60\degree$$  

• $$20\degree,70\degree,40\degree$$  

• $$90\degree,35\degree,45\degree$$  

• $$15\degree,75\degree,25\degree$$  

6) A bank teller has ₱2000 in₱20 and ₱10 coins. If the total number of coins is 122, how many of each type does she have?

​

Let x be the no. of pieces of 10pesos, and

let 122 - x be the no. of pieces of 20pesos

​value of 10pesos + value of 20pesos = 2000

6) A bank teller has ₱2000 in₱20 and ₱10 coins. If the total number of coins is 122, how many of each type does she have?

​

Let x be the no. of pieces of 10pesos, and

let 122 - x be the no. of pieces of 20pesos

​value of 10pesos + value of 20pesos = 2000

10x + 20(122 - x) = 2000​

10x + 2440 - 20x = 2000

-10x + 2440 = 2000

-10x = -440

x = 44​

6) A bank teller has ₱2000 in₱20 and ₱10 coins. If the total number of coins is 122, how many of each type does she have?

​

Let x be the no. of pieces of 10pesos, and

let 122 - x be the no. of pieces of 20pesos

​value of 10pesos + value of 20pesos = 2000

10x + 20(122 - x) = 2000​

10x + 2440 - 20x = 2000

-10x + 2440 = 2000

-10x = -440

x = 44​

Therefore, ​there are 44 pieces of 10pesos and 78 pieces of 20pesos.

6) A bank teller has ₱2000 in ₱20 and ₱10 coins. If the total number of coins is 122, how many of each type does she have?

​

7) A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?

​

Let x be the no. of pieces of 10pesos,

let 2x be the no. of pieces of 5pesos, and

let 2x - 14 be the no. of pieces of 1peso​​

​

7) A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?

​

Let x be the no. of pieces of 10pesos,

let 2x be the no. of pieces of 5pesos, and

let 2x - 14 be the no. of pieces of 1peso​​

10x + (5)2x + 1(2x - 14) = 1570

7) A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?

​

Let x be the no. of pieces of 10pesos,

let 2x be the no. of pieces of 5pesos, and

let 2x - 14 be the no. of pieces of 1peso​​

10x + (5)2x + 1(2x - 14) = 1570

10x + 10x + 2x - 14 = 1570

22x - 14 = 1570

22x = 1584

x = 72​

7) A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?

​

Let x be the no. of pieces of 10pesos,

let 2x be the no. of pieces of 5pesos, and

let 2x - 14 be the no. of pieces of 1peso​​

10x + (5)2x + 1(2x - 14) = 1570

10x + 10x + 2x - 14 = 1570

22x - 14 = 1570

22x = 1584

x = 72​

Therefore, ​there are 72 pieces of ₱10-coins, 144 pieces of ₱5-coins, and 130 pieces of ₱1-coins.

7) A coin bank for donations for the protection of the reef contained ₱1570. There were twice as many ₱5-coins as ₱10-coins, and 14 less ₱1-coins as ₱5-coins. How many of each kind were there?

​

Multiple Choice

A purse contains 27 coins in ₱1 and ₱5 and its total value is ₱83. Find the number of ₱1 and ₱5 coins in the purse.

• 13 pcs of ₱5

  14 pcs of ₱1

• 10 pcs of ₱5

  25 pcs of ₱1

• 14 pcs of ₱5

  13 pcs of ₱1

• 21 pcs of ₱5

  12 pcs of ₱1

Multiple Choice

Dave’s piggy bank consists of ₱5 and ₱10 coins only. There are thrice as many as ₱5 coins as there are ₱10 coins. If the coins are worth ₱300, how many coins of each kind are there?

• 10 pcs of ₱10

  25 pcs of ₱5

• 12 pcs of ₱10

  36 pcs of ₱5

• 10 pcs of ₱10

  15 pcs of ₱5

• 20 pcs of ₱10

  45 pcs of ₱5