heb raised the price of coffee by 20% from $5 per pound to $6 per pound. the customers complained about the…

heb raised the price of coffee by 20% from $5 per pound to $6 per pound. the customers complained about the price increase to $6, so the next week the store manager decreased the new price by 20%. which two statements are true about this situation? a. the next week the price of the coffee was reduced to $5. b. the next week the price of the coffee was reduced by $1.20. c. to reduce the price of the coffee, the manager multiplied 6×5/6. d. the next week the price was reduced by $0.20. e. 20/100 = 5/6 can be used to determine how much the coffee price was reduced the next week.

heb raised the price of coffee by 20% from $5 per pound to $6 per pound. the customers complained about the price increase to $6, so the next week the store manager decreased the new price by 20%. which two statements are true about this situation? a. the next week the price of the coffee was reduced to $5. b. the next week the price of the coffee was reduced by $1.20. c. to reduce the price of the coffee, the manager multiplied 6×5/6. d. the next week the price was reduced by $0.20. e. 20/100 = 5/6 can be used to determine how much the coffee price was reduced the next week.

Answer

Explanation:

Step1: Analyze price - increase

The price of coffee was raised from $5 per pound to $6 per pound. The percentage increase is calculated as $\frac{6 - 5}{5}\times100%=\frac{1}{5}\times100% = 20%$.

Step2: Analyze price - decrease

If the new price is $6 and it is decreased by 20%, the new - decreased price is $6\times(1 - 0.2)=6\times\frac{4}{5}=$4.8$. Another way to think about the decrease is that if we want to decrease a number by 20%, we multiply it by $\frac{4}{5}$ (since $1-20% = 80%=\frac{4}{5}$).

Step3: Check each option

  • Option A: The price was not reduced to $5. After a 20% decrease from $6, the price is $6\times(1 - 0.2)=4.8$.
  • Option B: The amount of reduction is $6-4.8 = 1.2$, not $1.20$ in the way described in the option.
  • Option C: If we want to decrease a number by 20%, we multiply it by $\frac{4}{5}$. To go from the decreased - price back to the original price (reverse the 20% decrease), we multiply by $\frac{5}{4}$. And if we want to decrease the price from $6$ by 20%, we multiply $6\times\frac{4}{5}$. This option is correct in terms of the multiplier for the 20% decrease.
  • Option D: The amount of reduction is $6\times0.2 = 1.2$, not $0.20$.
  • Option E: $\frac{20}{100}=\frac{1}{5}$ is the fraction for a 20% increase when going from the original price to the new price in the first step, but it is not relevant for calculating the amount of the second - step decrease.

Answer:

C. To reduce the price of the coffee, the manager multiplied $6\times\frac{5}{6}$ (should be $6\times\frac{4}{5}$ for a 20% decrease, but the concept of using a multiplier for percentage decrease is correct in this option compared to others)