Algebra Math Number word problems using the linear system

Mathematics
Tutor: None Selected Time limit: 1 Day

The sum of three numbers is 8. Twice the smallest is 2 less than the largest, while the sum of the largest and smallest is 5. Use a linear system in three variables to find the three numbers.

Jun 14th, 2015

Thank you for the opportunity to help you with your question!

Let x = the smallest number

Let y = the middle number

Let z = the largest number

then,

x+y+z = 8

2x = z - 2

x + z = 5

Using substitution,

2(5-z) = z - 2

10 - 2z = z - 2

3z = 12

z = 4

x = 5 - 4 = 1

y = 8 - 4 - 1 = 3

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 14th, 2015

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