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**Conversion Factors/Relationships:**
- 1 mile = 1.61 kilometers
- 1 gallon = 3.78 liters
- 2,000 pounds = 1 ton
- 2.20 pounds = 1 kilogram

1. Convert 9.85 L to gallons.
2. How many miles are in 25 km?
3. If a person has a mass of 60 kilograms, what is their mass in tons?

Answer :

you can easily understand converstion factors with a rule of thee

Step 1

a) Convert 9.85 L to gallons.

Let

x number of gallons

if

1 gallon = 3.78 liters

xgallon = 9.85 liters

Step 2

do the relation and solve for x

[tex]\begin{gathered} \frac{1}{3.78}=\frac{x}{9.85} \\ \text{solve for x} \\ 3.78\cdot x=1\cdot9.85 \\ x=\frac{9.85}{3.78} \\ x=2.60 \end{gathered}[/tex]

so, 9.85 L= 2.6 gallons

b)How many miles are in 25 km?

1 mile = 1.61 kilometer

Let

x number of miles

if

1 mile = 1.61 km

x mile = 25 Km

Step 2

do the relation and solve for x

[tex]\begin{gathered} \frac{1}{1.61}=\frac{x}{25} \\ \text{multiplied both sides by 25} \\ 25\cdot\frac{1}{1.61}=25\cdot\frac{x}{25} \\ x=\frac{25}{1.61} \\ x=15.52 \end{gathered}[/tex]

so, 25 Km= 15.52 miles

c)If a person has a mass of 60 kilograms, what is his mass in tons?

if

2,000 pounds = 1 ton

2.20 pounds = 1 kilogram

then

first, convert kilogram to pounds, then convert pounds to tons?

Let x, number of pounds

2.20 pounds = 1 kilogram

x pounds = 60 Kilogram

[tex]\begin{gathered} \frac{2.2}{1}=\frac{x}{60} \\ \text{solve for x} \\ x=60\cdot2.2 \\ x=132 \end{gathered}[/tex]

so , 60 Kg=132 pounds

Now, convert pounds to tons

Let x, number of tons

2,000 pounds = 1 ton

132 Pounds = x ton

[tex]\begin{gathered} \frac{2000}{1}=\frac{132}{x} \\ \text{solve for x} \\ 2000\cdot x=132\cdot1 \\ 2000x=132 \\ x=\frac{132}{2000} \\ x=\text{0}.066 \end{gathered}[/tex]

so, 60 Kg =0.066 tons

I hope this helps you

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