Question

1. un médico prescribió a sergio una pastilla diaria para controlar su presión arterial. la siguiente imagen muestra el empaque de pastillas que sergio adquirió.

luego de unos días de tomar responsablemente sus pastillas sergio se ha dado cuenta de que ya ha tomado mas de \frac{1}{2} del total de pastillas del empaque pero menos de \frac{2}{3}. cuántos días lleva sergio tomando sus pastillas?

Explanation:

🆕 New Concept Discovered: Finding Fractions of a Set
Finding a portion of a total group

Step 1: Count the total number of pills

First, we count the total number of pills in the package shown in the image. The blister pack has 3 rows and 4 columns of pills:

$$ \text{Total pills} = 3 \times 4 = 12 $$

Since Sergio takes 1 pill per day, the number of days he has been taking them is equal to the number of pills he has consumed.

Step 2: Calculate the lower limit

We are told he has taken more than \( \frac{1}{2} \) of the total pills. Let's find what \( \frac{1}{2} \) of the total is:

$$ \frac{1}{2} \times 12 = 6 $$

Since he has taken more than this amount, the number of days must be strictly greater than 6:

$$ \text{Days} > 6 $$

Step 3: Calculate the upper limit

We are also told he has taken less than \( \frac{2}{3} \) of the total pills. Let's find what \( \frac{2}{3} \) of the total is:

$$ \frac{2}{3} \times 12 = \frac{24}{3} = 8 $$

Since he has taken less than this amount, the number of days must be strictly less than 8:

$$ \text{Days} < 8 $$

Step 4: Find the integer value

The number of days must be a whole number that is strictly between 6 and 8:

$$ 6 < \text{Days} < 8 $$

The only integer that satisfies this inequality is 7.

Answer:

Sergio lleva 7 días tomando sus pastillas.