The expression 8x+2(3y) represents the total amount, in dollars, that Davellyn spent on tank tops and scarves, where x represents the number of tank tops she bought and y represents the number of scarves she bought. Which statement must be true about the amount Davellyn spent?
- She spent 8x dollars on scarves
- She spent 8 dollars for each scarf
- She spent 6y dollars on scarves
- She spent a total of 14 dollars
The Correct Answer and Explanation is:
The correct answer is:
She spent 6y dollars on scarves.
Explanation:
The given expression is:
[
8x + 2(3y)
]
where:
- (x) represents the number of tank tops Davellyn bought, and
- (y) represents the number of scarves Davellyn bought.
The expression breaks down into two parts:
- (8x): This part of the expression represents the amount spent on tank tops. If Davellyn spent 8 dollars per tank top and bought (x) tank tops, then the total amount spent on tank tops is (8x).
- (2(3y)): This part of the expression represents the amount spent on scarves. Let’s break it down:
- The factor (3y) indicates that each scarf costs 3 dollars.
- The factor of 2 outside the parentheses suggests that the amount of money Davellyn spent on scarves is then multiplied by 2. Therefore, Davellyn spends 6 dollars per scarf (because (3 \times 2 = 6)).
Thus, the total amount spent on scarves is (6y) dollars, where (y) represents the number of scarves.
Clarification of Each Statement:
- She spent 8x dollars on scarves: This is incorrect because the (8x) represents the money spent on tank tops, not scarves.
- She spent 8 dollars for each scarf: This is incorrect because the price of each scarf is 6 dollars, not 8.
- She spent 6y dollars on scarves: This is the correct statement. Since each scarf costs 6 dollars, the total spent on scarves is (6y) dollars, where (y) is the number of scarves.
- She spent a total of 14 dollars: This is incorrect because the total amount spent depends on both the number of tank tops and scarves Davellyn bought. It is not fixed at 14 dollars unless specific values for (x) and (y) are provided.
In conclusion, the total amount spent on scarves is represented by (6y) dollars, as each scarf costs 6 dollars, and Davellyn bought (y) scarves.