Final answer:
To solve this problem, we can set up a system of equations. The first number is 301 and the second number is 35.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's call the first number 'x' and the second number 'y'. We are given two pieces of information. The first is that the two numbers add up to 336, so we have the equation:
x + y = 336
The second piece of information is that the first number is 126 bigger than five times the second number. This can be expressed as the equation:
x = 5y + 126
We can solve these two equations simultaneously to find the values of 'x' and 'y'. Rearrange the second equation to make 'y' the subject:
y = (x - 126)/5
Substitute this expression for 'y' into the first equation:
x + (x - 126)/5 = 336
Now solve for 'x' by multiplying both sides by 5 to eliminate the fraction:
5x + x - 126 = 1680
Combine like terms:
6x - 126 = 1680
Add 126 to both sides:
6x = 1806
Divide by 6 to isolate 'x':
x = 301
Now substitute this value of 'x' back into either equation to find 'y'. Using the first equation:
301 + y = 336
Subtract 301 from both sides:
y = 35
So the two numbers are 301 and 35.