The sum of three numbers is 75. the first number is 7 more than the third. the second number is 2 times the third. what are the numbers

Let be the three numbers. We know that the first number is 7 more than the third, which means

Also, we know that the second number is 2 times the third, which means

Finally, we know that the three numbers sum up to 75, but we can rewrite the sum in terms of the third numbers, because the two previous equations gave us a way to express and in terms of :

Now, we can use those same equations to deduce the other two numbers:

the correct answer is 5 6 and 7