Video Transcript
Last year a family’s total income
was 46,000 dollars, while their total expenses were 48,100 dollars. Use the expression 𝐼 minus 𝐸 over
12, where 𝐼 represents the total income and 𝐸 represents the total expenses, to
find the average difference between the family’s income and its expenses each
month.
In this question, we are told that
a family made a total income of 46,000 dollars last year. And their total expenses that year
was 48,100 dollars. We are told to use the expression
𝐼 minus 𝐸 over 12 to find the average difference in income and expenses each month
for that year, where 𝐼 is the total income that year and 𝐸 is the total expenses
that year.
To evaluate this expression, we
first note that the value of 𝐼 will be 46,000 dollars and the value of 𝐸 will be
48,100 dollars. We can see that the numerator of
the expression is the total income for the year minus the total expenditure. This means it gives us the net
income of the family for that year. Substituting these values into the
expression gives us 46,000 dollars minus 48,100 dollars all over 12.
Remember, when using fraction
notation, we want to evaluate the expressions in the numerator and denominator
before the division. So we will start by evaluating the
subtraction in the numerator. We can calculate that 46,000 minus
48,100 is negative 2,100. So the family lost 2,100 dollars
last year. If we divide this loss by 12, then
we find the average loss of the family each month.
We can calculate that negative
2,100 dollars divided by 12 is negative 175 dollars. This means that the average
difference between the family’s income and expenses each month last year was
negative 175 dollars.
