Question

The sum of three numbers is 11. Two times the smallest is 1 less than the largest, while the sum of the largest and smallest is 7.Use a linear system in three variables to find the three numbers.

Answer 1

The numbers are 2, 4 and 5

STEP-BY-STEP EXPLANATION:

let x be the smallest, y the one that follows and z the largest

we have the following equations

`\begin{gathered} x+y+z=11 \\ z-1=2x \\ x+z=7 \end{gathered}`

We solve the system of equations as follows

`\begin{gathered} z-1=2x\rightarrow z=2x+1 \\ x+z=7\rightarrow z=7-x \\ \text{ we equate noth equations} \\ 2x+1=7-x \\ 2x+x=7-1 \\ 3x=6 \\ x=(6)/(3)=2 \end{gathered}`

now, for z:

`\begin{gathered} z=7-2 \\ z=5 \end{gathered}`

for y:

`\begin{gathered} 2+y+5=11 \\ y=11-5-2 \\ y=4 \end{gathered}`