Question

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

Answer 1

Let $a,b,c$ be the three numbers. We know that the first number is 7 more than the third, which means $a = c+7$

Also, we know that the second number is 2 times the third, which means $b = 2c$

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 $a$ and $b$ in terms of $c$:

$a+b+c = 75 \iff (c+7)+(2c)+c=75 \iff 4c+7 = 75 \iff 4c = 68 \iff c = 17$

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

$a = c+7 \implies a = 17+7 = 24,\quad b = 2c \implies b = 2\cdot 17 = 34$