Question

Two positive integers are in the ratio 1:3. If their sum is added to their product, the result is 224. Find the integers.

Answer 1

The answers are 8, 24. How?

Answer 2

Well, you can see that 24 = 3(8). That's where the 1:3 comes from. There are 3 8's for every 24, in a sense. The second part of the question: " If their sum is added to their product, the result is 224" is explained by the sum (8+24) = 32 is added to the product (8*24) = 192.
32 +192 = 224.
Does that make sense?

Answer 3

call the numbers x and y.
so, the numbers are in the ratio 1:3. this means:\[\frac{x}{y}=\frac{1}{3}\tag{a}\]
secondly, their sum plus their product is 224, so:\[x+y+xy=224\tag{b}\]
now from equation (a) we get:\[y=3x\tag{c}\]substitute the expression for y from equation (c) into equation (b) and solve for x. then use that solution to get the value for y from equation (c) and you are done.