Answer: the numbers are 10 and 80
Step-by-step explanation:
Let x represent the larger number.
Let y represent the smaller number.
One number is 8 times another number. This means that
x = 8y
The numbers are both positive and have a difference of 70. This means that
x - y = 70 - - - - - - - - - - - - - - - 1
Substituting x = 8y into equation 1, it becomes
8y - y = 70
7y = 70
Dividing the left hand side and the right hand side of the equation by 7, it becomes
7y/7 = 70/7
y = 10
Substituting y = 10 into x = 8y, it becomes
x = 8 × 10
x = 80
