What is the larger number if one number is eight more than twice another and their difference is 25?

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To solve the problem, let’s define the two numbers involved. Let x be the first number and y be the second number.

According to the problem, we have the following relationships:

  • One number (let’s say x) is eight more than twice another number (which is y):
    • x = 2y + 8
  • The difference between the two numbers is 25:
    • x - y = 25

Now, we can substitute the expression for x from the first equation into the second equation:

(2y + 8) - y = 25

This simplifies to:

2y + 8 - y = 25
y + 8 = 25

Next, we isolate y:

y = 25 - 8
y = 17

Now that we have the value of y, we can substitute it back into the first equation to find x:

x = 2(17) + 8
x = 34 + 8
x = 42

So, the larger number is 42.

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