Solving a rate problem
Solving a rate problem
If gas is 66 cents per L, what is this in dollars per gallon?
If gas is 66 cents per L, what is this in dollars per gallon?
In this problem we have two units: “cents” and “gallons”
If gas is 66 cents per L, what is this in dollars per gallon?
We have to be able to turn the words “66 cents per liter” into
a term we can use in a calculation.
66centsper liter = 66cents/ liter 

66cents
1l
Now we can begin our calculation:
We first write what we are given
66cents
1l

We will be changing both given units, cents and liters, in this problem
We will now change one unit at a time to
the desired unit.
66cents
1l

We will now change one unit at a time to
the desired unit.
66cents

1l

Remember, we always multiply
We will now change one unit at a time to
the desired unit.
66cents

1l
It does not matter which one we start with so we will start
with liters.

We will now change one unit at a time to
the desired unit.
66cents

1l
We start by writing liters on the top of the next term.

We will now change one unit at a time to the
desired unit.
66cents 1l

1l

We start by writing liters on the top of the next term.
We will now change one unit at a time to the
desired unit.
66cents 1l

1l

On the bottom we will place the units we want to replace for liters, qt.
66cents
1l


1l
1.08qt
Now we put quarts on the bottom

66cents
1l


1l
1.08qt
We put 1.08 in front of qt since 1l = 1.08 qt.

We have now converted liters into quarts.
66cents
1l


1l
1.08qt

66cents
1l


1l
1.08qt
Now we will convert quarts into gallons

We put qt on the top of the 3rd term
66cents
1l
qt


1l
1.08qt
Now we will convert quarts into gallons

Then we put gal on the bottom
66cents
1l
qt


1l
1.08qt gal
Now we will convert quarts into gallons

Now we are ready to put numbers in front of the units
66cents
1l
qt


1l
1.08qt gal
Now we will convert quarts into gallons

Now we are ready to put numbers in front of the units
66cents
1l
4qt


1l
1.08qt 1gal
Now we are ready to put numbers in front of the units
66cents
1l
4qt


1l
1.08qt 1gal
Since we know that 1 gal = 4 qt. , those
are the numbers we place in front of those units
We are half way done. We have converted one of the
units, liters, into gallons.
66cents
1l
4qt


1l
1.08qt 1gal

We are half way done. We have converted one of the
Units, liters, into gallons.
66cents
1l
4qt


1l
1.08qt 1gal
Now we will change cents into dollars

On the bottom of the 4th term we put the units “cents”
66cents
1l
4qt




1l
1.08qt 1gal cents

On the bottom of the 4th term we put the units “cents”
66cents
1l
4qt




1l
1.08qt 1gal cents
Cents on the bottom of the 4th term will factor out
with cents on the top of the first term.
Dollars are the unit that we want to factor in.
66cents
1l
4qt dollars



1l
1.08qt 1gal cents

Dollars are the unit that we want to factor in.
66cents
1l
4qt dollars =



1l
1.08qt 1gal cents
So dollars go on top of the 4th term.

Now we need to put numbers in front of the units
of the 4th term.
66cents
1l
4qt dollars =



1l
1.08qt 1gal cents
Now we need to put numbers in front of the units
of the 4th term.
66cents
1l
4qt 1dollar =



1l
1.08qt 1gal 100cents

We know that 1 dollar = 100 cents. So those
are the appropriate numbers.
When we factor the units we are left with dollars/gallon
66cents
1l
4qt 1dollar
dollars




1l
1.08qt 1gal 100cents gallon

When we factor the units we are left with dollars/gallon
66cents
1l
4qt 1dollar
dollars




1l
1.08qt 1gal 100cents gallon

Those are the units we want.
When we factor the units we are left with dollars/gallon
66cents
1l
4qt 1dollar
dollars




1l
1.08qt 1gal 100cents gallon

Those are the units we want.
Now we can “do the math”
When we do the math,
66cents
1l
4qt 1dollar
2.4dollars




1l
1.08qt 1gal 100cents
gallon

When we do the math,
66cents
1l
4qt 1dollar
2.4dollars




1l
1.08qt 1gal 100cents
gallon
everything on the bottom gets divided,

When we do the math,
66cents
1l
4qt 1dollar
2.4dollars




1l
1.08qt 1gal 100cents
gallon
everything on the bottom gets divided,

and everything on top gets multiplied
When we do the math,
66cents
1l
4qt 1dollar
2.4dollars




1l
1.08qt 1gal 100cents
gallon
into our calculator, we put 66 / 1.08 x 4 / 100

Our fewest number of significant digits is 2
from “66cents”, so we have only 2 digits in our answer
2.4
66cents
1l
4qt 1dollar
2.4dollars




1l
1.08qt 1gal 100cents
gallon
into our calculator, we put 66 / 1.08 x 4 / 100

Another way of showing our answer would be
66cents
1l
4qt 1dollar



 2.4dollars gallon
1l
1.08qt 1gal 100cents

Another way of showing our answer would be
66cents
1l
4qt 1dollar



 2.4dollars gallon
1l
1.08qt 1gal 100cents

This would be the same as saying
2.4 dollars per gallon.
If gas is 66 cents per L, what is this in dollars per gallon?
66cents
1l
4qt 1dollar



 2.4dollars gallon
1l
1.08qt 1gal 100cents