Write a system of linear equations in three variables, and then use matrices to solve the system.
-There were approximately 100,000 vehicles sold at a particular dealership last year. The dealer tracks sales by age group for marketing purposes. The percentage of 36- to 59-year-old buyers and the percentage of buyers 60 and older combined exceeds the percentage of buyers 35 and younger by 40%. If the percentage of buyers in the oldest group is doubled, it is 34% less than the percentage of users in the middle group. Find the percentage of buyers in each of the three age groups.
A) 30% 35 and younger; 58% 36-59 year olds; 12% 60 and older
B) 32% 35 and younger; 55% 36-59 year olds; 13% 60 and older
C) 24% 35 and younger; 60% 36-59 year olds; 16% 60 and older
D) 12% 35 and younger; 58% 36-59 year olds; 30% 60 and older

Question

Quizplus · Accepted Answer

The system of equations based on the given information is:1. $x + y + z = 100$ (where $x$ is the percentage of buyers 35 and younger, $y$ is the percentage of buyers 36-59, and $z$ is the percentage of buyers 60 and older, all adding up to 100%).2. $y + z = x + 40$ (the percentage of 36- to 59-year-olds and 60+ exceeds the percentage of ≤35 by 40%).3. $2z = y - 34$ (doubling the oldest group's percentage is 34% less than the middle group's percentage).Solving this system using matrices or substitution/elimination methods yields $x = 30$, $y = 58$, and $z = 12$, which corresponds to choice A.

Write a System of Linear Equations in Three Variables, and Then