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

heb raised the price of coffee by 20% from $5 per pound to $6 per pound. the customers complained 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 = 6/x 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 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 = 6/x can be used to determine how much the coffee price was reduced the next week.

Answer

Explanation:

Step1: Analyze the price - change situation

The price of coffee was raised from $5 to $6, a 20% increase ($\frac{6 - 5}{5}\times100%=20%$). Then the manager decreased the new price ($6) by 20%.

Step2: Calculate the new - decreased price

The formula for percentage decrease is $P = P_0(1 - r)$, where $P_0$ is the original price and $r$ is the rate of decrease. Here, $P_0 = 6$ and $r=0.2$. So $P = 6\times(1 - 0.2)=6\times0.8 = 4.8$. The amount of decrease is $6-4.8 = 1.2$.

Step3: Check each option

  • Option A: The price was increased to $6$, not reduced to $5$. So A is false.
  • Option B: The amount of decrease is $6\times0.2=1.2$, not $1.20$ in the sense of a non - percentage amount reduction from an incorrect base. So B is false.
  • Option C: If we want to go back from the increased price of $6$ to the price before the decrease, we know that if $6$ is the 100% price and we want to find the price after a 20% decrease, we multiply by $\frac{5}{6}$ (since $1-0.2=\frac{4}{5}$, and to reverse the operation we use its reciprocal $\frac{5}{6}$). This option is correct.
  • Option D: The price was decreased by $6\times0.2 = 1.2$, not $0.20$. So D is false.
  • Option E: $\frac{20}{100}$ is the rate of increase or decrease, not a way to directly determine the amount of price reduction in this context. So E is false.

Answer:

C. To reduce the price of the coffee, the manager multiplied $6\times\frac{5}{6}$