Question 362970
it was a nosebleed, but i think i found the solution.


you have 2 equations to work with.


they are:


3x + 4y = z
3a + 4b = z


you know that x = y, so you can replace y with x to get:


3x + 4x = z
3a + 4b = z


you can simplify this to get:


7x = z
3a + 4b = z


since z equals to 7x, you can substitute for z to get:


3a + 4b = 7x


you know that a + b = x + y + 2


since x = y, this becomes:


a + b = 2x + 2


in your equation of 3a + 4b = z, you know that 3a = z/2 and you know that 4b = z/2 because you were given that the price for yellow bananas was equal to the total divided by 2, and the price for red bananas was equal to the total divided by 2.


you have 3a = z/2 and you have 4b = z/2


you know that z = 7x, so you can substitute to get:


3a = 7x/2 and 4b = 7x/2


you can solve for a to get a = 7x/6 and you can solve for b to get b = 7x/8


you know that a + b = 2x + 2


substitute for a and b in this equation to get:


7x/6 + 7x/8 = 2x + 2


multiply both sides of this equation by 48 to get:


56x + 42x = 96x + 96


simplify to get:


98x = 96x + 96


subtract 96x from both sides of the equation to get:


2x = 96


divide both sides of the equation by 2 to get:


x = 48


you now know that x = 48, and you can substitute in the first equation to get:


3*48 + 4*48 = 336


you can now substitute in the second equation to get:


3*a + 4*b = 336


you now know that a = 7x/6 which makes a = 7*48/6 which makes a = 7*8 = 56


you now know that b = 7x/8 which makes b = 7*48/8 which makes b = 7*6 = 42


you get a = 56 and b = 42 which is the answer you are looking for.


you confirm by substituting in the original equations.


x = y = 48
3x + 4y = 336
3*48 + 4*48 = 336
144 + 192 = 336
336 = 336 (good)


a = 56 and b = 42
3*56 + 4*42 = 336
168 + 168 = 336
336 = 336 (good)


end of nosebleed.