Keane has a total of 96 counters. some are green and some are red. the ratio of the number of red to number of green counters is 3 : 5. how many more green counters than red?

There are 24 more green counters than red

Solution:

Given that, Keane has a total of 96 counters

Some are green and some are red.

The ratio of the number of red to number of green counters is 3 : 5

number of red counters : number of green counters = 3 : 5

Let the number of red counters be 3x

Let the number of green counters be 5x

Total number of counters = 96

Therefore,

number of red counters + number of green counters = 96

3x + 5x = 96

8x = 96

x = 12

Number of red counters = 3x = 3(12) = 36

Number of green counters = 5x = 5(12) = 60

Number of green counters than red = number of green counters - number of red counters

Number of green counters than red = 60 - 36 = 24

Thus there are 24 more green counters than red

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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