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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

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

Question 1:

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

The cost of the oranges can be calculated as: \[ 3 \times 0.89 \text{ dollars} \] The total cost for the apples is: \[ 4x \text{ dollars} \] The total cost equation would be: \[ 3(0.89) + 4x = 7.15 \] This simplifies to: \[ 4x + 3(0.89) = 7.15 \] So, the correct equation to find the cost of each apple is: A: \(4x + 3(0.89) = 7.15\)

Question 2:

Next, we want to determine the sequence of arithmetic operations to solve for \(x\). From the equation we have: \[ 4x + 3(0.89) = 7.15 \] First, we can subtract \(3(0.89)\) from both sides: \[ 4x = 7.15 - 3(0.89) \] Next, we would divide the result by 4: \[ x = \frac{7.15 - 3(0.89)}{4} \] This means:

  • Subtract \(3(0.89)\) from \(7.15\)
  • Divide the difference by 4

Thus, the sequence of operations that could be used to solve for the cost of each apple is: D: Multiply \(0.89\) by \(3\); subtract product from \(7.15\); divide difference by \(4\) (Here the operations are logically implied, as the first operation involves calculating \(3(0.89)\) first).

Summary of Answers:

Question 1: A
Question 2: D