Gerad has a wooden board 11 feet long, he wants to cut it into 2 pieces so that the longer piece is 4 feet less than 4 times the length of the shorter piece, how long will each piece be

Shorter piece is 3 ft, longer piece is 8 ft

Step-by-step explanation:

Set up two equations...

Let x be the length of the shorter piece, and let y be the length of the longer piece.

The whole board is 11 feet long, so

x + y = 11

He wants the longer piece to be 4 feet less than 4 times the length of the shorter board, so

y = 4x - 4

Substitute the second equation into the first equation

x + 4x - 4 = 11           (y becomes 4x - 4)

Now solve for x

5x = 15                 (combine like terms, add 4 to both sides)

   x = 3                (divide both sides by 5)

Now substitute 3 in for x in either equation and solve for y...

y = 4(3) - 4

    y = 12 - 4

            y  =  8

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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