Question

peter has twice as many stickers as joe. joe has 40 more stickers than Emily. They have 300 altogether. How many stickers does Peter have?

Answer 1

Peter has 170 joe has 85 and Emily has 45

Answer 2

Answer: Peter has 170 stickers.

Step-by-step explanation: Given that Peter has twice as many stickers as Joe, Joe has 40 more stickers than Emily and they have 300 altogether.

We are to find the number of stickers that Peter have.

Let x, y and z represents the number of stickers that Peter, Joe and Emily has respectively.

Then, according to the given information, we have

`x=2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=z+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\x+y+z=300~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x and y from equations (i) and (ii) in equation (iii), we get

`2y+z+40+z=300\\\\\Rightarrow 2(z+40)+2z+40=300\\\\\Rightarrow 2z+80+2z+40=300\\\\\Rightarrow 4z+120=300\\\\\Rightarrow 4z=300-120\\\\\Rightarrow 4z=180\\\\\Rightarrow z=(180)/(4)\\\\\Rightarrow z=45.`

From equation (ii), we get

`y=45+40=85`

and from equation (i), we get

`x=2*85=170.`

Thus, Peter has 170 stickers.