In a small town, there are two main sections called the hill section and the lake section. the town has a population of 4298.the number of people who live in hill section is 188 more than twice the number of people who live in the lake section. how many people live in each section of the town.

Let x be the number of people in Hill section

Let y be the number of people in Lake section

The town has a population of 4298.

x + y = 4298     > first equation

The number of people live in Hill section is 188 more than twice the number of people live in the lake section

Hill section = 2 (lake section) + 188

x = 2y + 11  > second equation

Plug in second equation in first equation

x + y = 4298

2y + 11 + y = 4298

3y + 11 = 4298 (subtract 11 on both sides)

3y = 4287 (divide both sides by 3)

y = 1429

x = 2y + 11  > second equation

Plug in y in the second equation

x = 2(1429) + 11  

x = 2858 +11

x= 2869

The number of people in Hill section= 2869

The number of people in Lake section= 1429

99

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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