Question

use a system of equations to solve the following problem. the sum of three integers is 393. the sum of the first and second integers exceeds the third by 39. the third integer is 26 less than the first. find the three integers. answerhow to enter your answer (opens in new window) 5 points first integer = second integer = third integer =

Explanation:

Step1: Define variables

Let the first integer be $x$, the second be $y$, and the third be $z$.
We have the following system of equations:
$x + y+z = 393$ (sum of three - integers is 393)
$x + y=z + 39$ (sum of first and second exceeds the third by 39)
$z=x - 26$ (third is 26 less than the first)

Step2: Substitute $z=x - 26$ into $x + y=z + 39$

$x + y=(x - 26)+39$
$x + y=x+13$
$y = 13$

Step3: Substitute $y = 13$ and $z=x - 26$ into $x + y+z = 393$

$x+13+(x - 26)=393$
$x+13+x - 26 = 393$
$2x-13 = 393$
$2x=393 + 13$
$2x=406$
$x = 203$

Step4: Find $z$

Since $z=x - 26$, then $z=203 - 26=177$

Answer:

first integer = 203
second integer = 13
third integer = 177