The price of a dozen eggs was $1.63. Suppose the price increases m dollars per dozen and then the price decreases $0.12 per dozen. Which expression represents the current price of eggs after the two price changes?
Responses
A m + 0.51m + 0.51
B m + 1.51m + 1.51
C m + 1.63m + 1.63
D m + 1.75m + 1.75
E m + 2.83
A m + 0.51m + 0.51
B m + 1.51m + 1.51
C m + 1.63m + 1.63
D m + 1.75m + 1.75
E m + 2.83
The correct expression is m + 1.51. This is because the price first increases by m dollars, making the price 1.63 + m dollars per dozen. Then the price decreases by $0.12 per dozen, making the final price 1.63 + m - 0.12 = m + 1.51 dollars per dozen. Therefore the answer choice is not in the options, none of the response is correct.
To find the current price of eggs after the two price changes, we can start with the initial price of $1.63 and then apply the two changes.
First, the price increases m dollars per dozen. So, the price after the first change would be:
$1.63 + m
Next, the price decreases $0.12 per dozen. So, the price after the second change would be:
$1.63 + m - 0.12
Combining these two changes, the expression that represents the current price of eggs after the two price changes is:
$1.63 + m - 0.12
Simplifying this expression, we get:
$1.51 + m
Therefore, the correct answer is B) m + 1.51m + 1.51.
To determine the current price of eggs after the two price changes, let's break down the given information step by step.
1. The initial price of a dozen eggs was $1.63.
2. The price then increased by m dollars per dozen, so the new price is $1.63 + m.
3. After the price increase, the price decreases by $0.12 per dozen. Therefore, we subtract $0.12 from the new price calculated in step 2: ($1.63 + m) - 0.12.
Combining these steps, the expression representing the current price of eggs after two price changes is ($1.63 + m) - 0.12, which simplifies to $1.63 + m - 0.12.
Now, let's compare this expression to the given options:
A. m + 0.51m + 0.51: This expression does not match the simplified expression.
B. m + 1.51m + 1.51: This expression does not match the simplified expression.
C. m + 1.63m + 1.63: This expression matches the simplified expression. Hence, it represents the current price of eggs.
D. m + 1.75m + 1.75: This expression does not match the simplified expression.
E. m + 2.83: This expression does not match the simplified expression.
Therefore, the correct answer is C. m + 1.63m + 1.63.