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Core Connections Geometry, 2013

CC

Core Connections Geometry, 2013 View details

1. Section 3.1

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Exercise 31 Page 158

Practice makes perfect

a To solve the proportion, we will start by using cross products.

14/5=x/3

Cross multiply

14(3)=5(x)

Multiply

42=5x

From here, we will continue solving for x by using the Properties of Equality.

42=5x

Rearrange equation

5x=42

.LHS /5.=.RHS /5.

x=42/5

Use a calculator

x=8.4

The solution to the equation is x=8.4. We can check our solution by substituting it into the original equation.

14/5=x/3

x= 8.4

14/5 ? = 8.4/3

▼

Simplify

a/b=a * 3/b * 3

42/15 ? = 8.4/3

a/b=a * 5/b * 5

42/15=42/15 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

b To solve the proportion, we will start by using cross products. Then we will continue solving for m by using the Properties of Equality.

10/m=5/11

Cross multiply

10(11)=5(m)

Multiply

110=5m

Rearrange equation

5m=110

.LHS /5.=.RHS /5.

m=22

The solution to the equation is m=22. We can check our solution by substituting it into the original equation.

10/m=5/11

m= 22

10/22 ? = 5/11

a/b=.a /2./.b /2.

5/11=5/11 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

c To solve the proportion, we will start by using cross products. Remember that we will need to treat t-2 as a single quantity in the cross multiplication process.

t-2/12=7/8

Cross multiply

8(t-2)=12(7)

Multiply

8(t-2)=84

From here, we will continue solving for t by using the Distributive Property and the Properties of Equality.

8(t-2)=84

Distribute 8

8t-16=84

LHS+16=RHS+16

8t=100

.LHS /8.=.RHS /8.

t=100/8

Use a calculator

t=12.5

The solution to the equation is t=12.5. We can check our solution by substituting it into the original equation.

t-2/12=7/8

t= 12.5

12.5-2/12=7/8

▼

Simplify

Subtract term

10.5/12=7/8

a/b=a * 2/b * 2

21/24=7/8

a/b=a * 3/b * 3

21/24=21/24 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

d To solve the proportion, we will start by using cross products. Remember that we will need to treat x+1 as a single quantity in the cross multiplication process.

x+1/5=x/3

Cross multiply

3(x+1)=5(x)

Multiply

3(x+1)=5x

From here, we will continue solving for x by using the Distributive Property and the Properties of Equality.

3(x+1)=5x

Distribute 3

3x+3=5x

LHS-3x=RHS-3x

3=2x

Rearrange equation

2x=3

.LHS /2.=.RHS /2.

x=3/2

Use a calculator

x=1.5

The solution to the equation is x=1.5. We can check our solution by substituting it into the original equation.

x+1/5=x/3

x= 1.5

1.5+1/5 ? = 1.5/3

▼

Simplify

Add terms

2.5/5 ? = 1.5/3

a/b=a * 3/b * 3

7.5/15 ? = 1.5/3

a/b=a * 5/b * 5

7.5/15=7.5/15 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

3.1.1 Dilations p.148-149

3.1.2 Similarity p.154-155

3.1.3 Using Ratios of Similarity p.158-159

3.1.4 Applications and Notation p.164-165