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.
Correct answer : (1)
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.
Correct answer : (4)
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.]
Correct answer : (2)
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.
Correct answer : (3)
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.
Correct answer : (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 [Add 1 to both sides.]
x = 0 [Simplify.]
So the value of x is zero.
Correct answer : (3)
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.
Correct answer : (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 [Add 5 on both sides.]
4x = 20 [Simplify.]
4x4 = 204 [Divide by 4 on both sides.]
The value of x is 5.
Correct answer : (1)
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.]
Correct answer : (4)
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.]