The problem states that the cooking time for meat is 13 minutes for every 500 grams of meat plus 20 minutes. (a) We need to calculate the time it takes to cook 1.5 kg of meat. (b) We need to find a formula for the total cooking time $T$ for $M$ grams of meat.

1. Problem Description

The problem states that the cooking time for meat is 13 minutes for every 500 grams of meat plus 20 minutes.

(a) We need to calculate the time it takes to cook 1.5 kg of meat.

(b) We need to find a formula for the total cooking time $T$ for $M$ grams of meat.

2. Solution Steps

(a) First, convert 1.5 kg to grams.

$1 \text{ kg} = 1000 \text{ g}$, so $1.5 \text{ kg} = 1.5 \times 1000 = 1500 \text{ g}$.

Next, determine how many 500-gram portions are in 1500 grams.

$\text{Number of 500g portions} = \frac{1500}{500} = 3$.

For each 500-gram portion, it takes 13 minutes to cook.

So for 3 portions, it takes $3 \times 13 = 39$ minutes.

Then, add the additional 20 minutes: $39 + 20 = 59$ minutes.

(b) Let $T$ be the total cooking time in minutes and $M$ be the mass of the meat in grams.

The number of 500-gram portions is $\frac{M}{500}$.

The cooking time for $\frac{M}{500}$ portions is $13 \times \frac{M}{500}$.

Adding the extra 20 minutes, we get

$T = 13 \times \frac{M}{500} + 20 = \frac{13M}{500} + 20$.

3. Final Answer

(a) 59 minutes

(b) $T = \frac{13M}{500} + 20$