Answer :
Certainly! Let's solve the problem step-by-step:
1. Initial Reduction:
- The magazine cover is first photocopied using a scale factor of \(\frac{1}{2}\).
- This means that every dimension (length and width) of the cover is reduced to half of its original size.
- For example, if the original dimensions were \( L \) and \( W \), the dimensions after this reduction would be \(\frac{L}{2}\) and \(\frac{W}{2}\).
2. Enlargement by a Factor of 3:
- After the initial reduction, the photocopied cover is then enlarged by a factor of 3.
- Enlarging by a factor of 3 means that each dimension of the reduced cover is multiplied by 3.
- Continuing from our previous dimensions, \(\frac{L}{2}\) and \(\frac{W}{2}\), after enlarging by a factor of 3, the new dimensions would be:
[tex]\[ 3 \times \frac{L}{2} = \frac{3L}{2} \][/tex]
[tex]\[ 3 \times \frac{W}{2} = \frac{3W}{2} \][/tex]
To find the overall scale factor resulting from these two steps, we need to multiply the scale factors of each step.
3. Calculating the Overall Scale Factor:
- The initial scale factor is \(\frac{1}{2}\).
- Then we apply the enlargement factor of 3. The overall scale factor is:
[tex]\[ \frac{1}{2} \times 3 = \frac{3}{2} = 1.5 \][/tex]
Thus, after the given process of reduction and subsequent enlargement, the final scale factor is 1.5. This means that the final dimensions of the magazine cover are 1.5 times the original dimensions.
So, in conclusion, the overall scale factor applied to the magazine cover after both operations is 1.5.
1. Initial Reduction:
- The magazine cover is first photocopied using a scale factor of \(\frac{1}{2}\).
- This means that every dimension (length and width) of the cover is reduced to half of its original size.
- For example, if the original dimensions were \( L \) and \( W \), the dimensions after this reduction would be \(\frac{L}{2}\) and \(\frac{W}{2}\).
2. Enlargement by a Factor of 3:
- After the initial reduction, the photocopied cover is then enlarged by a factor of 3.
- Enlarging by a factor of 3 means that each dimension of the reduced cover is multiplied by 3.
- Continuing from our previous dimensions, \(\frac{L}{2}\) and \(\frac{W}{2}\), after enlarging by a factor of 3, the new dimensions would be:
[tex]\[ 3 \times \frac{L}{2} = \frac{3L}{2} \][/tex]
[tex]\[ 3 \times \frac{W}{2} = \frac{3W}{2} \][/tex]
To find the overall scale factor resulting from these two steps, we need to multiply the scale factors of each step.
3. Calculating the Overall Scale Factor:
- The initial scale factor is \(\frac{1}{2}\).
- Then we apply the enlargement factor of 3. The overall scale factor is:
[tex]\[ \frac{1}{2} \times 3 = \frac{3}{2} = 1.5 \][/tex]
Thus, after the given process of reduction and subsequent enlargement, the final scale factor is 1.5. This means that the final dimensions of the magazine cover are 1.5 times the original dimensions.
So, in conclusion, the overall scale factor applied to the magazine cover after both operations is 1.5.
