Finding Solutions
Hangers!
Area Diagrams + Distributive Property
Percents
Some extra problems :)
100
Is x = 4 a solution to 3x + 3 = 2 ?
No!
3 • 4 + 3 = 15
100
Write an equation to go with hanger A.
3x = 11
or
3 • x = 11
100
Write an expression to show the area of the rectangle.
5(10 + 4)
100
Write an equation that shows the relationship 10% of 120 is x.
0.10 • 120 = x
or
10/100 • 120 = x
100
Ms. Sowder is selling raffle tickets for $1.25 per ticket. How much would she earn if she sold 30 tickets?
1.25 • 30 = 37.50
200
Is x = 2 a solution to 2x – 2 = 2 ?
Yes!
200
Write the equation to go with hanger B.
11 = y + 5
or
y + 5 = 11
200
Write an expression to show the area of the rectangle.
3(x + 5)
200
Write an equation that shows the relationship 12% of x is 30.
0.12 • x = 30
or
12/100 • x = 30
200
Ms. Sowder is selling raffle tickets for $1.25 per ticket. How much would she earn if she sold r tickets? (HINT: Write an expression)
1.25r
or 1.25 • r
300
Is x = 3 a solution to 9x = 19 ?
No!
9 • 3 = 18
300
Write an equation to go with the hanger.
5x + 2 = 17
300
Write an expression to show the area of the rectangle AND use the distributive property to show how you could find the area.
6(3 + 2) = 6 • 3 + 6 • 2 = 18 + 12 = 30
300
Write an equation that shows the relationship 20% of 140 is x.
0.20 • 140 = x
or
20/100 • 140 = x
300
How many tickets ($1.25 each) would Ms. Sowder need to sell to earn $62.50?
1.25 • r = 62.50
divide both sides by 1.25
r = 62.50/1.25
do the division
r = 50
400
If x = 2, does this make the following equation true or false?
3x – 1 = 5 ?
TRUE!
400
Write an equation to go with hanger C.
11 = 4z
400
The expression for this area model is z(11 + 4). Write TWO more expressions that would represent the area.
1. z • 11 + z • 4
2. z • 15
3. 11z + 4z
400
Write an equation that shows the relationship 32% of x is 40.
0.32 • x = 40
or
32/100 • x = 40
400
Ms. Clark filled her hydroflask with 2oz of La Croix, which was 1/6 of her hydroflask. The whole hydroflask holds 19 oz. Which diagram represents this situation?
Diagram C
500
If x = 6, does this make the following equation true or false?
x/3 + 1 = 4 ?
TRUE!
500
Write the equation to go with hanger D.
13 4/5 = w + 3 4/5
500
Write THREE expressions to represent the area of this area diagram.
1. 7(x + 10)
2. 7 • x + 7 • 10
3. 7x + 70
500
45% of z is 72. Find the value of z.
45/100 • z = 72
divide by 45/100 on both sides
72 ÷ 45/100 <–– divide by a fraction = keep change flip
72 • 100/45 = 7200/45 simplify
800/5 = 160 = z
500
Write the equation that represents the tape diagram and SOLVE it!
x + 4 = 17
subtract 4 from both sides
x = 13