Final answer:
The two numbers are 18 and 72, where 18 is the smaller number and 72 is four times the smaller number, which add up to 90.
Step-by-step explanation:
To solve the problem where the sum of two numbers is 90 and one number is 4 times the other, we first let one number be x. According to the problem, the other number will then be 4x. The sum of the two numbers gives us our first equation:
x + 4x = 90
Combining like terms, we have:
5x = 90
Dividing both sides of the equation by 5 to solve for x, we get:
x = 18
So, one number is 18. To find the other number, we multiply 18 by 4:
4 × 18 = 72
Therefore, the two numbers are 18 and 72.