Help im stuck with this math question: Solving Probelms using algebraic modelling?

Question

A crate of 36 grape fruit has a total mass of 4 kg. When 12 grape fruit are removed, the total mass is 3 kg. determine the mass of the crate and the mass of one grapefruit.--- can u tell let x equal ??....let y equal ??...and what are the 2 equations?? thanks for taking ur tyme

Answer 1

Let x = weight of crate, and y = weight of grapefruit.

Your equations are:

x + 36y = 4 kg ← the weight of the crate to begin with

x + 24y = 3 kg ← the weight after 12 grapefruit are removed

So, subtract the second equation from the first to solve for y:

x + 36y = 4 kg
x + 24y = 3 kg
------------------------
0x + 12y = 1 kg

y = 1/12 kg

Now substitute this value for y into either of your original two equations, to solve for x:

x + 36y = 4 kg

x + 36(1/12 kg) = 4 kg

x + 3 kg = 4 kg

x = 1 kg

~ ~ ~ ~ ~

So the crate weighs x = 1 kg
And each grapefruit weighs y = 1/12 kg

Hope that helped!

~ ♥ ~

Answer 2

Let the crate weigh x
Let the grapefruit weigh y

Now we know that x + 36y = 4kg
And x + 24y = 3kg
(from simple deduction, we also know that 12y = 1kg)
y = 1/12kg, or about 0.83kg.

Substitutite that into either first equation and solve for x

x + 36y =4
x + 3 = 4
x = 1 kg

Check with the other equation:

x + 24y = 3
x + 2 = 3
x = 1 kg

Crate is 1 kg, each grapfruit is 1/12kg.

Answer 3

let the mass of the cratebe x
and the mass of grape y
x+36y=4
x+24y=3
subtracting
12y=1
y=1/12 kg
mass of 1 grape fruit=1/12 kg
substituting
x+3=4
x=1
mass of crate=1 kg