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 38%. If the percentage
Of buyers in the oldest group is doubled, it is 24% less than the percentage of users in the middle group.
Find the percentage of buyers in each of the three age groups.
A)31% 35 and younger; 54% 36-59 year olds; 15% 60 and older
B)33% 35 and younger; 51% 36-59 year olds; 16% 60 and older
C)25% 35 and younger; 56% 36-59 year olds; 19% 60 and older
D)15% 35 and younger; 54% 36-59 year olds; 31% 60 and older

Question

Quizplus · Accepted Answer

Let $x$, $y$, and $z$ represent the percentages of buyers 35 and younger, 36-59 years old, and 60 and older, respectively. The system of equations based on the given information is:1. $x + y + z = 100$ (since all percentages must add up to 100%)2. $y + z = x + 38$ (the sum of the middle and oldest groups exceeds the youngest by 38%)3. $2z = y - 24$ (doubling the oldest group's percentage is 24% less than the middle group's percentage)Solving this system using matrices or substitution yields $x = 31$, $y = 54$, and $z = 15$, which corresponds to choice A.

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