Solve the simultaneous equations.
Given that x and y are positive integers, solve the simultaneous equations:
3^x * 2^y = 72
3^(x-1) * 2^(y+1) = 48
A box of marbles
A box contains red, blue, and green marbles. There are twice as many red marbles as blue marbles, and there are 5 more green marbles than blue marbles. If the total number of marbles is 37, how many of each colour marble are there?
Given:
ReplyDelete3^x * 2^y = 72
3^(x-1) * 2^(y+1) = 48
First, let's simplify the second equation:
3^(x-1) * 2^(y+1) = 48
=> 3^x / 3 * 2^y * 2 = 48
=> 3^x * 2^y = 48 * 3 / 2
=> 3^x * 2^y = 72
Now, we have two equations:
3^x * 2^y = 144
3^x * 2^y = 144
This means that there are infinite solutions.