The ratio of boys to girls at north middle school is 3 boys to every 4 girls. if the seventh grade has 120 girls, how many total students are in the seventh grade?

There are 210 students in 7th grade. 90+120=210. You have to cross multiply by setting up two proportions (3/4 and x/120) and multiply 3 by 120 and multiply 4 by x. That leaves you with 360 on one side and 4x on the other. In order to find the value of x you have to isolate it by dividing both sides by 4 to get rid of the 4 on the side that has x. And you do 360/4=90. Then just add the amount of boys with the amount of girls to get your total.

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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