## anonymous 4 years ago Two positive integers are in the ratio 1:3. If their sum is added to their product, the result is 224. Find the integers.

1. anonymous

The answers are 8, 24. How?

2. anonymous

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?

3. asnaseer

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.

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