Question

The sum of three numbers is 97. The third number is 9 less than the first. The second number is 2 times the third. What are the numbers

Answer 1

Explanation:

x + y + z = 97 eq1

x - z = 9 eq2

y = 2z eq3

Since y is already defined in eq3, we can substitute eq3 into eq1.

x + 2z + z = 97

x + 3z = 97 new eq1

Now, we have only 2 equations to work with that have two variables.

x + 3z = 97 new eq1

x - z = 9 eq2

Subtract eq2 from new eq1 to eliminate the x terms.

4z = 88

z = 22

Next, substitute this value of z into eq3 to solve for y.

y = 2(22)

y = 44

Finally, we can substitute the values of y and z into eq1 to solve for x.

x = 97 - 44 - 22

x = 31

The three numbers are 22, 31, and 44.