The product of two integers is 50. one integer is twice the other. find the integers.

Use what they are telling. 

a*b=50 (one integer times the other give you a product of 50. we're randomly calling these integers "a" and "b")

2a=b (one integer is twice the amount of the other. we're randomly selecting "b" to be twice the amount of "a")

plug in what we know 

a*(2a)=50 (we replaced "b" with "2a" because we know from the info they gave us that b=2a)

now solve for "a"

a*2a=50
2a²=50
a²=50/2
a²=25
√a²=√25
a=5

which because 2a=b we know that b=10