Question

Conversion Factors/ Relationships1 mile = 1.61 kilometer1 gallon = 3.78 liters2,000 pounds = 1 ton2.20 pounds = 1 kilogramConvert 9.85 L to gallons.How many miles are in 25 km?If a person has a mass of 60 kilograms, what is his mass in tons?

Answer 1

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

`\begin{gathered} (1)/(3.78)=(x)/(9.85) \\ \text{solve for x} \\ 3.78\cdot x=1\cdot9.85 \\ x=(9.85)/(3.78) \\ x=2.60 \end{gathered}`

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

`\begin{gathered} (1)/(1.61)=(x)/(25) \\ \text{multiplied both sides by 25} \\ 25\cdot(1)/(1.61)=25\cdot(x)/(25) \\ x=(25)/(1.61) \\ x=15.52 \end{gathered}`

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

`\begin{gathered} (2.2)/(1)=(x)/(60) \\ \text{solve for x} \\ x=60\cdot2.2 \\ x=132 \end{gathered}`

so , 60 Kg=132 pounds

Now, convert pounds to tons

Let x, number of tons

2,000 pounds = 1 ton

132 Pounds = x ton

`\begin{gathered} (2000)/(1)=(132)/(x) \\ \text{solve for x} \\ 2000\cdot x=132\cdot1 \\ 2000x=132 \\ x=(132)/(2000) \\ x=\text{0}.066 \end{gathered}`

so, 60 Kg =0.066 tons

I hope this helps you