Question

In the last few months, local news channels have been featuring stories about price increases in Cincinnati during the pandemic. The monthly cost of cable TV for some families increased from $56 to $62. The average cost of a dozen eggs increased from $1.59 to $2.39.

(A) Calculate the absolute change in the monthly cost of cable TV. Round to the nearest whole number.

(B) Calculate the relative change in the monthly cost of cable TV. Round to the nearest whole number.

(C) Calculate the absolute change in the cost of a dozen eggs. Round to two decimal places.

(D) Calculate the relative change in the cost of the dozen eggs. Round to the nearest whole number.

(E) A cable customer feels that the monthly cost of cable TV increased the most. A grocery customer feels that the cost of a dozen eggs increased the most. Is it possible for both customers to be correct? Explain your response in one of two complete sentences. ​

Answer 1

(A) The absolute change in the monthly cost of cable TV is $6.

(B) The relative change in the monthly cost of cable TV is 11%.

(C) The absolute change in the cost of a dozen eggs is $0.80.

(D) The relative change in the cost of a dozen eggs is 50%.

(E) Yes, both customers can be correct. The cable customer is correct in terms of absolute change, while the grocery customer is correct in terms of relative change. Absolute change measures the difference between two values, while relative change measures the proportional difference between two values. Since the initial cost of cable TV was higher than that of a dozen eggs, it makes sense that the absolute increase in cable TV cost would be greater than that of eggs. However, since the initial cost of eggs was lower than that of cable TV, it makes sense that the relative increase in egg cost would be greater than that of cable TV.

Explanation:

(A) The absolute change in the monthly cost of cable TV is calculated by subtracting the initial cost from the final cost.

Absolute change = Final cost - Initial cost

Substituting the given values, we get:

Absolute change = $62 - $56 = $6

Therefore, the absolute change in the monthly cost of cable TV is $6.

(B) The relative change in the monthly cost of cable TV is calculated by dividing the absolute change by the initial cost and multiplying by 100 to express it as a percentage.

Relative change = (Absolute change / Initial cost) x 100%

Substituting the given values, we get:

Relative change = ($6 / $56) x 100% = 10.71%

Therefore, the relative change in the monthly cost of cable TV is 11% (rounded to the nearest whole number).

(C) The absolute change in the cost of a dozen eggs is calculated by subtracting the initial price from the final price.

Absolute change = Final price - Initial price

Substituting the given values, we get:

Absolute change = $2.39 - $1.59 = $0.80

Therefore, the absolute change in the cost of a dozen eggs is $0.80.

(D) The relative change in the cost of a dozen eggs is calculated by dividing the absolute change by the initial price and multiplying by 100 to express it as a percentage.

Relative change = (Absolute change / Initial price) x 100%

Substituting the given values, we get:

Relative change = ($0.80 / $1.59) x 100% = 50.31%

Therefore, the relative change in the cost of a dozen eggs is 50% (rounded to the nearest whole number).