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 $\frac{5}{6}\times6$. d. the next week the price was reduced by $0.20. e. $\frac{20}{100}$ 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 $\frac{5}{6}\times6$. d. the next week the price was reduced by $0.20. e. $\frac{20}{100}$ can be used to determine how much the coffee price was reduced the next week.

Answer

Explanation:

Step1: Calculate the new - price after the increase

The original price of coffee is $5$ per pound. It is raised by 20% to $6$. The formula for percentage increase is $P_{new}=P_{old}(1 + r)$, where $P_{old}=5$ and $r = 0.2$. So $P_{new}=5\times(1 + 0.2)=6$.

Step2: Analyze the reduction

The manager decreases the new price ($6$) by 20%. The formula for percentage decrease is $P_{final}=P_{new}(1 - r)$. Here, $P_{new}=6$ and $r = 0.2$, so $P_{final}=6\times(1 - 0.2)=6\times0.8 = 4.8$. The amount of reduction is $6-4.8 = 1.2$.

Step3: Check each option

  • Option A: The price was not reduced to $5$.
  • Option B: The price was reduced by $6 - 4.8=1.2$, not $1.20$ in the sense of a non - percentage amount reduction description in this option.
  • Option C: To find the reduced price, we multiply the new price ($6$) by $\frac{4}{5}$ (since $1 - 0.2=\frac{4}{5}$), $6\times\frac{4}{5}=4.8$. This option is correct.
  • Option D: The price was not reduced by $0.20$ in the way described.
  • Option E: $\frac{20}{100}\times6 = 1.2$ is the amount of reduction, not a way to find the final price as described in the option.

Answer:

C. To reduce the price of the coffee, the manager multiplied $6\times\frac{4}{5}$