Final answer:
To find the larger number, we can set up a system of equations based on the given information. Let x be the smaller number and y be the larger number. From the first statement, y - x = 8. From the second statement, 5x + y = 98. Solving this system of equations, we find that the larger number is 23.
Step-by-step explanation:
To find the larger number, we can set up a system of equations based on the given information.
Let's say the smaller number is x and the larger number is y.
From the first statement, we know that y - x = 8.
From the second statement, we know that 5x + y = 98.
We can solve this system of equations to find the values of x and y. Plugging in the value of y from the first equation into the second equation, we get:
5x + (x + 8) = 98
Simplifying, we get:
6x + 8 = 98
Subtracting 8 from both sides, we get:
6x = 90
Dividing by 6, we get:
x = 15
Now, plugging x = 15 into the first equation, we get:
y - 15 = 8
Adding 15 to both sides, we get:
y = 23
Therefore, the larger number is 23.