Algebra Word Problems Worksheet - Page 2

Algebra Word Problems Worksheet
• Page 2
11.
Find the value of $y$ in the equation $y$ + 2 = 4 using algebra tiles.
 a. 2 b. 7 c. 6 d. 3

Solution:

The model for the linear equation is
[One y-tile and two 1-tiles on the left side and four 1-tiles on the right side.]

[Isolate the variable.]

[Remove two 1-tiles from both sides to show the value of y.]

The value of y is 2.

12.
Chris and his son caught 6 fish. How many fish did his son catch, if Chris caught 4 fish? Solve using algebra tiles.
 a. 3 b. 4 c. 6 d. 2

Solution:

Let y be the number of fish caught by Chris's son.

The equation for the total number of fish caught by Chris and his son is 4 + y = 6
[Write the linear equation.]

Represent the equation in the form of algebra tiles.
[One variable tile and four 1-tiles on left side and six 1-tiles on the right side.]

[Make a group of four 1-tiles on each side to isolate the variable tile.]

[Remove the grouped 1-tiles on both sides to show the value of variable y.]

The number of fish caught by Chris's son is 2.

13.
Two packets of rice together weigh 5 kg. If one packet weighs 2 kg, then what is the weight of the other packet? Solve using algebra tiles.
 a. 2 kg b. 3 kg c. 9 kg d. 5 kg

Solution:

Let y be the weight of the other packet.

y + 2 = 5
[Write the algebraic equation for the total weight of the two packets.]

Represent the equation in the form of algebra tiles.
[One variable tile and two 1-tiles on the left side and five 1-tiles on the right side.]

[Isolate the variable tile by subtracting two 1-tiles on each side.]

[Remove the grouped 1-tiles to show the value of y.]

So, the weight of the other packet is 3 kg.
[Three 1-tiles represent 3 kg.]

14.
Identify an algebraic equation for the algebra tiles and solve for the value of $x$.

 a. -2 b. 2 c. -4 d. -3

Solution:

4x = 5x + 4
[Original equation.]

4x - 5x = 5x + 4 - 5x
[Subtract 5x from both sides.]

-x = 4
[Simplify.]

x = -4
[Multiply on both sides with -1.]

The value of x is -4.

15.
Identify an algebraic equation for the algebra tiles and solve for the value of $x$.

 a. 2 b. 5 c. 3 d. 4

Solution:

2x + 6 = 4x + 2 - 2
[Original equation.]

2x + 6 = 4x
[Simplify on the right hand side.]

2x + 6 - 4x = 4x - 4x
[Subtract 4x from both sides.]

-2x + 6 = 0
[Simplify.]

-2x + 6 - 6 = 0 - 6
[Subtract 6 from both sides.]

-2x = -6
[Simplify.]

x = 3
[Divide each side by -2.]

The value of x is 3.

16.
Find the value of $x$ for the algebra tiles.

 a. 2 b. 4 c. 5

Solution:

3x + 3 - 4 = 2x + 2 - 3
[Original equation.]

3x - 1 = 2x - 1
[Simplify.]

3x - 1 - 2x = 2x - 1 - 2x
[Subtract 2x from both sides.]

x - 1 = -1
[Simplify.]

x - 1 + 1 = - 1 + 1

x = 0
[Simplify.]

So the value of x is zero.

17.
Find the value of $x$, from the algebra tiles.

 a. 2 b. 5 c. 3 d. 4

Solution:

In the model, the left hand side contains two variable x-tiles and two +1 tiles, the right hand side has one variable x-tile and five +1 tiles.

The linear equation for the model is 2x + 2 = x + 5
[Two x tiles represent 2x, two +1 tiles represent +2, one x tile represent x and five +1 tiles represent +5.]

x + 2 = 5
[Subtract x from both sides.]

x + 2 - 2 = 5 - 2
[Subtract 2 from both sides.]

x = 3

So, the value of the variable x is 3.

18.
Identify an equation for the algebra tiles and solve the equation for the value of $x$.

 a. 5 b. 3 c. 4 d. 6

Solution:

5x - 5 = x + 15
[Original equation.]

5x - 5 - x = x + 15 - x
[Subtract x from both sides.]

4x - 5 + 5 = 15 + 5

4x = 20
[Simplify.]

4x4 = 204
[Divide by 4 on both sides.]

The value of x is 5.

19.
Two packets of sugar together weigh 5 kg. If one packet weighs 2 kg, then what is the weight of the other packet? Solve using algebra tiles.
 a. 9 kg b. 5 kg c. 2 kg d. 3 kg

Solution:

Let y be the weight of the other packet.

y + 2 = 5
[Write the algebraic equation for the total weight of the two packets.]

Represent the equation in the form of algebra tiles.
[One variable tile and two 1-tiles on the left side and five 1-tiles on the right side.]

[Isolate the variable tile by subtracting two 1-tiles on each side.]

[Remove the grouped 1-tiles to show the value of y.]

So, the weight of the other packet is 3 kg.
[Three 1-tiles represent 3 kg.]

20.
Mr. Henry bought a box containing 20 doughnuts and distributed evenly among 5 members in his family. How many doughnuts did each of the five members receive? Solve using algebra tiles.
 a. 7 b. 6 c. 5 d. 4

Solution:

Total number of doughnuts to be distributed among 5 family members evenly is 20.

Let x be the number of doughnuts that each family member gets.

5x = 20
[Original equation.]

[Represent the equation in the form of algebra tiles.]

[Isolate each side into five parts.]

[Take one part from each side.]

So, each family member gets 4 doughnuts.