A photocopier enlarges by a ratio of 7:4. A picture measures 6 cm by 4 cm. How many consecutive enlargements can be made so that the largest possible picture will fit on a sheet measuring 30 cm by 20 cm?
4 * [(7/4)^n] = 20
Hi scott, Thank you for your answer. Can you please explain it?
4 (the short side) is multiplied by 7/4 (the enlarging factor) n times to equal 20 (the short side of the large sheet)
4 * 7/4 * 7/4 ... = 20
n is probably not an integer , so just round it down to the next whole number
... no fractional enlargements
you can start with 4 and keep multiplying by 7/4 until you hit 20
... just count the number of multiplications
To solve this problem, we need to find how many consecutive enlargements can be made while ensuring that the largest possible picture will fit on the given sheet.
First, let's calculate the dimensions of the largest possible picture after each enlargement:
1st enlargement: 6 cm x (7/4) = 10.5 cm x 4 cm
2nd enlargement: 10.5 cm x (7/4) = 18.375 cm x 4 cm
3rd enlargement: 18.375 cm x (7/4) = 32.15625 cm x 4 cm
It's important to note that the photocopier enlarges the picture by a ratio of 7:4. This means that each time we enlarge it, the dimensions of the picture are multiplied by (7/4).
Now, let's determine how many consecutive enlargements can be made. We'll work with the width dimension since it's the limiting factor in this case.
Starting with the original picture width of 6 cm, we'll calculate the new width after each enlargement:
1st enlargement: 6 cm x (7/4) = 10.5 cm
2nd enlargement: 10.5 cm x (7/4) = 18.375 cm
3rd enlargement: 18.375 cm x (7/4) = 32.15625 cm
After the third enlargement, the width of the picture is 32.15625 cm. Since this width is larger than the width of the given sheet (30 cm), we cannot make any more consecutive enlargements.
Therefore, the maximum number of consecutive enlargements that can be made is 3.