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 4

Answer 1

Let's break down the problem step by step to answer both questions.

Question 1

Ben bought 3 oranges for 89 cents each and 4 apples for \( x \) dollars each. The total amount spent is $7.15.

1. The cost of the 3 oranges can be calculated as: \[ 3 \times 0.89 \] This equals \( 2.67 \) dollars.

2. The total cost is given as \( 7.15 \) dollars. Therefore, if we let \( x \) be the cost of each apple, the equation representing the total spending becomes: \[ 4x + 3(0.89) = 7.15 \] Thus, the correct option for Question 1 is: A: \( 4x + 3(0.89) = 7.15 \)

Question 2

To find the cost of each apple \( x \), we'll follow these arithmetic steps based on the equation we just established:

1. Calculate the cost spent on oranges: \[ 3(0.89) = 2.67 \]

2. Subtract this amount from the total amount spent ($7.15): \[ 7.15 - 2.67 \]

3. Divide the resulting amount by 4 to find the cost of each apple: \[ \text{Cost of each apple} = \frac{7.15 - 2.67}{4} \]

Based on the above steps, the corresponding option is: A: Subtract 0.89 from $7.15; divide difference by 4

Final Answers:

• Question 1: A
• Question 2: A