One week, Isabelle bought 2 bags of apples and 3 bags of oranges. The next week, she bought 1 bag of apples and 2 bags of oranges. If a represents the cost of each bag of apples and r represents the cost of each bag of oranges, which expression could Isabelle use to calculate the difference between the amounts she spent each week?

Verified Answer :

Answer:

\(-a-r\) OR \(a+r\)

Step-by-step explanation:


First week cost of Isabelle:

2 bags of apples at a price of \(a\) each, so total cost is \(2a\)

3 bags of oranges at a price of \(r\) each, so total cost is \(3r\)

Sum of these two: \(2a+3r\)


Second week cost of Isabelle:

1 bag of apple at a price of \(a\) each, so total cost is \(a\)

2 bags of oranges at a price of \(r\) each, so total cost is \(2r\)

Sum of these two: \(a+2r\)


Depending on the price of bags of apples and oranges, the second week can cost more, or the first week's total could be more.


  • If 2nd weeks total is more than 1st week's total:

The difference is 2nd week's total minus first week's total:

\((a+2r)-(2a+3r)\\=-a-r\)

  • If 1st weeks total is more than 2nd week's total:

The difference is 1st week's total minus second week's total:

\((2a+3r)-(a+2r)\\=a+r\)


Answer: D (2a+3r)-(a +2r)

Step-by-step explanation:

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