Comparing Algebraic and Arithmetic Solutions

Question

Ben bought 3 oranges for 89 cents each and 4 apples for x dollars each. He spent $7.15 for the apples and oranges.
Question 1
Which equation could be used to find the cost of each apple?
Responses
A 4x + 3(0.89) = $7.154x + 3(0.89) = $7.15
B 3x + 4(0.89) = $7.153x + 4(0.89) = $7.15
C $7.15 − 3x = 0.89$7.15 − 3x = 0.89
D 4x − 3(0.89) = $7.154x − 3(0.89) = $7.15
Question 2
Which sequence of arithmetic operations could be used to solve for the cost of each apple?
Responses
A Subtract 0.89 from $7.15; divide difference by 4Subtract 0.89 from $7.15; divide difference by 4
B Subtract 0.89 from $7.15; divide difference by 7Subtract 0.89 from $7.15; divide difference by 7
C Multiply 0.89 by 3; add product to $7.15; divide sum by 4Multiply 0.89 by 3; add product to $7.15; divide sum by 4
D Multiply 0.89 by 3; subtract product from $7.15; divide difference by 4Multiply 0.89 by 3; subtract product from $7.15; divide difference by 4
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Answer 1

To solve the problem, let's analyze it step by step.

Question 1

Scenario: Ben bought 3 oranges at 89 cents each and 4 apples at \( x \) dollars each, spending a total of $7.15.

Calculating the cost of the oranges: The cost of 3 oranges can be calculated as: \[ 3 \times 0.89 = 2.67 \]

Total cost setup: Therefore, the total cost equation accounting for both the oranges and apples is: \[ 4x + 3(0.89) = 7.15 \] This can be simplified by calculating the total cost of the oranges: \[ 4x + 2.67 = 7.15 \]

Therefore, the correct equation to find the cost of each apple (x) is: Response A: \( 4x + 3(0.89) = 7.15 \)

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Question 2

Steps to solve for \( x \):

1. Start with the equation: \( 4x + 2.67 = 7.15 \).
2. Subtract \( 2.67 \) from both sides: \[ 4x = 7.15 - 2.67 \]
3. Calculate \( 7.15 - 2.67 = 4.48 \): \[ 4x = 4.48 \]
4. Finally, divide both sides by 4 to find \( x \): \[ x = \frac{4.48}{4} \]

The sequence of operations that we followed involved subtracting the cost of the oranges from the total cost and then dividing by the number of apples.

Thus, the correct arithmetic operation to find \( x \) is: Response D: Multiply \( 0.89 \) by 3; subtract product from $7.15; divide difference by 4.

In summary:

• For Question 1, the answer is A.
• For Question 2, the answer is D.