Question Video: Evaluating Algebraic Expressions in a Real-World Context | Nagwa Question Video: Evaluating Algebraic Expressions in a Real-World Context | Nagwa

Question Video: Evaluating Algebraic Expressions in a Real-World Context Mathematics • First Year of Preparatory School

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Last year a family’s total income was $46,000, while their total expenses were $48,100. Use the expression (𝐼 − 𝐸)/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.

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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.

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