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Rewrite Expressions
Hailey just had lunch at the Sushi Palace, and she wants to leave an 18% tip. She writes the expression b + 0.18b to compute her bill with a tip, where b is her bill before the tip.
Question 1
Which expression is equivalent to Hailey's expression?
Responses
A 1.18b
1.18b
B 0.18(2b)0.18(2b)
C 1.18(2b)1.18(2b)
D 2(1.18b)2(1.18b)
Question 2
After lunch, Hailey goes to the pet store. Suppose Hailey buys 5 guinea pigs at 20% off the original price of g dollars per guinea pig, which expression will NOT give Hailey's total cost?
Responses
A 4g4g
B 5g - 0.205g - 0.20
C 5g − 0.2(5g)5g − 0.2(5g)
D 5g − 1g
Question 1
The expression equivalent to Hailey's expression is A 1.18b. This is because the original expression (b + 0.18b) can be simplified by using the distributive property, which gives 1b + 0.18b or simply 1.18b.
Question 2
The expression A 4g4g will NOT give Hailey's total cost. This is because this expression implies that Hailey bought 4 guinea pigs at the original price, not 5 at a discount of 20%.
Question 1:
The expression b + 0.18b can be simplified by combining like terms. The coefficient of b is 1 + 0.18, which is equal to 1.18. Therefore, the equivalent expression is 1.18b. So, the correct answer is A) 1.18b.
Question 2:
To find Hailey's total cost, we need to calculate the discounted price for each guinea pig (20% off the original price) and multiply it by the number of guinea pigs bought (5). Let's analyze each option:
A) 4g: This expression simply represents the original price of 4 guinea pigs and doesn't account for the discount or the number of guinea pigs bought. Therefore, it is not the correct answer.
B) 5g - 0.20: This expression represents the original price of 5 guinea pigs (5g) minus a discount of 20% (0.20). This correctly calculates Hailey's total cost after the discount, so it is not the correct answer.
C) 5g − 0.2(5g): This expression represents the original price of 5 guinea pigs (5g) minus a discount of 20% (0.2) multiplied by the original price. This correctly calculates Hailey's total cost after the discount, so it is not the correct answer.
D) 5g − 1g: This expression represents the original price of 5 guinea pigs (5g) minus a discount of 1g (which is not specified). This does not correctly calculate Hailey's total cost after the discount, so it is the correct answer.
Therefore, the correct answer is D) 5g - 1g.
To answer the first question, we need to find the expression that is equivalent to Hailey's expression, which is b + 0.18b.
Option A: 1.18b - This expression is the same as Hailey's expression since 1.18 is equal to 1 + 0.18, so this option is equivalent to b + 0.18b.
Option B: 0.18(2b) - This expression simplifies to 0.36b, which is not equivalent to Hailey's expression.
Option C: 1.18(2b) - This expression simplifies to 2.36b, which is not equivalent to Hailey's expression.
Option D: 2(1.18b) - This expression simplifies to 2.36b, which is not equivalent to Hailey's expression.
Therefore, the correct answer for Question 1 is option A, 1.18b.
Moving on to Question 2, we need to find the expression that will NOT give Hailey's total cost, considering she buys 5 guinea pigs at 20% off the original price of g dollars per guinea pig.
Option A: 4g - This expression does not account for the discount or the number of guinea pigs, so it is not suitable for calculating Hailey's total cost.
Option B: 5g - 0.205g - 0.20 - This expression accounts for the discount and the number of guinea pigs, so it is a possible option for calculating Hailey's total cost.
Option C: 5g - 0.2(5g) - This expression simplifies to 4g, which does not account for the discount or the number of guinea pigs, so it is not suitable for calculating Hailey's total cost.
Option D: 5g - 1g - This expression simplifies to 4g, which does not account for the discount or the number of guinea pigs, so it is not suitable for calculating Hailey's total cost.
Therefore, the correct answer for Question 2 is option A, 4g.
In summary:
Question 1: The expression equivalent to Hailey's expression is A, 1.18b.
Question 2: The expression that will NOT give Hailey's total cost is A, 4g.