Mathematics, 26.06.2019 22:30 adorsey846

At a large picnic, there were 45 dishes served altogether. every 3 people shared a dish of cole slaw between them. every 4 people shared a dish of potato salad between them. every 6 people shared a dish of hot dogs between them. how many people were at the picnic?

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Answer from: syd8152

There were 12·5=60 people at the picnic.

Step-by-step explanation:

If every 3 people shared a dish of Cole slaw between them, every 4 people shared a dish of potato salad between them and every 6 people shared a dish of hot dogs between them, then you can find the minimal number of people that can do such thing. Mathematically this is the least common multiplier LCM.

Since

3=3;4=2·2;6=2·3,

then LCM(3,4,6)=2·2·3=12.

Suppose at the picnic were 12 people. If every 3 people shared a dish of Cole slaw between them, then 12 : 3 = 4 such dishes were served. If every 4 people shared a dish of potato salad between them, then 12 : 4 = 3 such dishes were served. If every 6 people shared a dish of hot dogs between them, then 12 : 6 = 2 such dishes were served. In total, 4 + 3 + 2 =9 dishes.

You know there were 45 dishes served altogether. 45 is 5 times more than 9, then the number of people at the picnic is 5 times more than 12. Therefore, there were 12·5=60 people at the picnic.

Answer from: Quest

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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