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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

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 4

1 answer

To solve the problem step-by-step, let's analyze both questions.

Question 1:

Ben spent $7.15 in total for 3 oranges and 4 apples. The cost of the oranges is 89 cents each, so the total cost for oranges is: \[ 3 \times 0.89 = 2.67 \] Now, the total cost for the apples (which is 4 apples at $x each) can be expressed as: \[ 4x \] The overall equation for the total cost is: \[ 4x + 2.67 = 7.15 \]

We can rearrange this to isolate $x$: \[ 4x + 3(0.89) = 7.15 \] Thus, the correct equation that can be used to find the cost of each apple is: A: \( 4x + 3(0.89) = 7.15 \)

Question 2:

Now, we need to figure out how to solve for $x$. We start from the equation: \[ 4x + 3(0.89) = 7.15 \] First, calculate \( 3(0.89) \): \[ 3(0.89) = 2.67 \] This leads us to: \[ 4x + 2.67 = 7.15 \] Next, subtract \( 2.67 \) from \( 7.15 \): \[ 7.15 - 2.67 = 4.48 \] This leads us to: \[ 4x = 4.48 \] Finally, divide by 4 to solve for \( x \): \[ x = \frac{4.48}{4} = 1.12 \] The correct sequence of arithmetic operations to find the cost of each apple is: D: Multiply \( 0.89 \) by \( 3 \), subtract the product from \( 7.15 \), and divide the difference by \( 4 \).

Final Answers:

  1. A: \( 4x + 3(0.89) = 7.15 \)
  2. D: Multiply \( 0.89 \) by \( 3 \); subtract the product from \( 7.15 \); divide the difference by \( 4 \).