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Comparing Algebraic and Arithmetic Solutions

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

1 answer

Let's break down the problem to find the correct answers to both questions.

Given:

  • Ben bought 3 oranges at 89 cents each (which is $0.89 per orange).
  • He bought 4 apples at x dollars each.
  • The total cost of apples and oranges was $7.15.

First, we calculate the total cost of the oranges: \[ \text{Cost of oranges} = 3 \times 0.89 = 2.67 \text{ dollars} \]

Now, we can write the equation for the total cost: \[ 3(0.89) + 4x = 7.15 \] Substituting the cost of oranges: \[ 2.67 + 4x = 7.15 \]

We can rearrange this equation to solve for \(x\): \[ 4x = 7.15 - 2.67 \] \[ 4x = 4.48 \] \[ x = \frac{4.48}{4} = 1.12 \]

Question 1:

We need to find the equation that can be used to find the cost of each apple \(x\): The correct equation we derived is: \[ 4x + 3(0.89) = 7.15 \]

Thus, the answer is A: \[ 4x + 3(0.89) = 7.15 \]

Question 2:

To find the operations used to solve for \(x\), we can use the derived information:

  1. First, we subtract the total cost of oranges ($2.67) from the total amount spent ($7.15): \[ 7.15 - 2.67 = 4.48 \]
  2. Then, we divide the result by the number of apples (4): \[ x = \frac{4.48}{4} \]

Combining these two operations, we find:

  • Subtract the cost of oranges from $7.15 and then divide by 4 gives us the cost of each apple.

Thus, the correct sequence of operations is: D: Multiply 0.89 by 3; subtract product from $7.15; divide difference by 4.

Summary:

  • Question 1 answer: A
  • Question 2 answer: D