Question

Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.

Answer 1

Answer:

Step-by-step explanation:

We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:

y = 10x

Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:

2(x + y) = xy and we know that y = 10x so

2(x + 10x) = x(10x) and

$2(11x)=10x^2$ and

$10x^2-22x=0$ and

x(10x - 22) = 0 so

x = 0 or 10x - 22 = 0 which makes

x equal to $\frac{22}{10}=2.2$

So x = 2.2 and y = 22.