Question

Divide 33 photos into two groups so the ratio is 4:7.

Answer 1

To do this task the best way is always add both "sides" of ratio and divide whole group by this sum.
sum=4+7=11
33:11=3
Now we know how much is 1 and we can multiply by 4 and by 7 to find the answer.
3*4=12 - first group
3*7=21 - second group

Your result is ok.

Answer 2

The correct answer is:

12:21.

Explanation:

Let x be the part of our 33 photos that represents 4 in our ratio. Then the second part of the ratio, the part that represents 7, will be 33-x, the remaining number of photos.

This gives us the ratio

$\frac{x}{33-x}$

Since we know we want this ratio to equal 4:7, we can set up a proportion:

$\frac{x}{33-x}=\frac{4}{7}$

To solve this, we cross-multiply:

x(7) = (33-x)(4)

7x = (33-x)(4)

We use the distributive property on the right:

7x = 33*4-x*4

7x = 132-4x

Add 4x to each side:

7x+4x = 132-4x+4x

11x = 132

Divide both sies by 11:

11x/11 = 132/11

x = 12

The smaller portion of photos, that represents the 4 in our ratio, is 12. This leaves 33-x=33-12=21 for the larger portion of photos. This gives us the ratio 12:21.