One hundred and seven people get together in teams to take part in a quiz. Each team has three, four or five members. There are twenty-seven teams altogether and there are twice as many teams with four members as there are teams with three members. How many teams have five members?
One hundred and seven people get together in teams to take part in a quiz. Each team has three, four or five members. There are twenty-seven teams altogether and there are twice as many teams with four members as there are teams with three members. How many teams have five members?
Do you need help with this or is it just a challenge? If you need help, try writing the information as two equations, assigning letters to mentioned unknown quantities.
Do you need help with this or is it just a challenge? If you need help, try writing the information as two equations, assigning letters to mentioned unknown quantities.
I've literally done that but I don't know how to solve it. Could you explain how please?
I've literally done that but I don't know how to solve it. Could you explain how please?
If you have two simultaneous equations in x and y (say), one method is to solve for y in one equation and substitute that into the other equation to get an equation only in x. Another method is to multiply both equations by constants in such a way that when you subtract them, the ys or xs cancel out. Surprised you haven't learnt simultaneous equations in school yet. If you still don't understand it'd probably be best to look them up for a more comprehensive explanation.
If you have two simultaneous equations in x and y (say), one method is to solve for y in one equation and substitute that into the other equation to get an equation only in x. Another method is to multiply both equations by constants in such a way that when you subtract them, the ys or xs cancel out. Surprised you haven't learnt simultaneous equations in school yet. If you still don't understand it'd probably be best to look them up for a more comprehensive explanation.
I know how to solve simultaneous equations, I just dont know how to solve this problem which involes it , thats what I need explaning
I know how to solve simultaneous equations, I just dont know how to solve this problem which involes it , thats what I need explaning
Simple. You have teams of 3, 4 and 5. You do not know how many of each team therefore you assign variables to each and it has to sum up to 107 so 3x+4y+5z=107. Then you're told that the amount of teams is equal to 27 so x+y+z=27 and then you are ALSO told there are twice as many teams of 4 as there are of 3 so y=2x and you can simplify the two equations into 2 variables and solve it as normal.
would the equation be 3x+4y+5z=170 and 3x+4y+5z=27?
That wouldn't make sense as this system of equations is inconsistent; you'd get 0=143. Geometrically, these are 2 parallel planes so no intersections obviously.