Question

The sum of three numbers is 70. the third number is 3 times the first. The second number is 10 less than the firts. what are the numbers?First number=second number =Third number=

Answer 1

"The sum of three numbers is 70", this can be expressed as

$x+y+z=70$

"The third number is 3 times the first", we can express it as

$z=3x$

"The second number is 10 less than the first", this can be expressed as

$y=x-10$

Then, we combine all three equations

$\begin{gathered} x+y+z=70 \\ x+x-10+3x=70 \end{gathered}$

Let's solve for x

$\begin{gathered} 5x-10=70 \\ 5x=70+10 \\ x=\frac{80}{5} \\ x=16 \end{gathered}$

The first number is 16.

Then, we use this value to find y and z.

$\begin{gathered} y=x-10=16-10=6 \\ z=3x=3\cdot16=48 \end{gathered}$

The second number is 6.

The third number is 48.