Question

Yahya works at Target Pumpkin erasers cost $.60 each and ghost erasers cost $.40 each. He sold a total of 350 pumpkin and ghost erasers for $170.00. How many pumpkin erasers did Yahya sell?

Answer 1

`75` pumpkin erasers
`275` ghost erasers

Explanation:

let `x=`pumpkin erasers and `350-x=` ghost erasers.

`0.6x+0.4(350-x)=170`

`0.6x-0.4x+ 140=170`; distribute the `0.4`

`0.4x=30`; subtract `140` from both sides

`x=75`; divide both sides by `0.4`

`75` pumpkin erasers
`350-75` ghost erasers `=275`

Answer 2

150 pumpkin erasers

Explanation:

We can create a system of equations to represent this situation.

Pumpkin erasers cost `color(orange)($0.60)` each and ghost erasers cost `color(blue)($0.40)` each. In total, he sold `color(red)($170.00)` in erasers.

`color(orange)(.60)p + color(blue)(.40)g = color(red)(170)`

He sold 350 pumpkin and ghost erasers, so the number of ghost erasers plus the number of pumpkin erasers must equal 350.

`p + g = 350`

When solving a system of equations, the goal is to eliminate variables by adding the two equations together. Two of the same variables can only cancel out if they have the same coefficient but opposite signs (for example, 2x and -2x).

Let's multiply the second equation by `-.60`, so that `p` will become `-.60p`. Then, we can cancel out the variable `p` by adding the equations together.

`-.60 (p + g = 350)`
`-.60p -.60g = - 210`

Now add the equations together:

`cancel(.60p) + .40g = 170`
`cancel(-.60p) -.60g = - 210`

`-.2g = -40`

Divide both sides by `-.2` to find `g`.

`g = 200`

If `200` ghost erasers were sold, then the number of pumpkin erasers must be `150`.

`350 - 200 = 150`

Hope this helps!

Answer 3

A very different approach just for the hell of it. The explanations takes a lot longer than the actual maths.

count of $0.6 rubbers is 150 `larr`pumpkin erasers
count of $0.4 rubbers is 200

Explanation:

This does use the principles used by the other contributors but just looks different.

Let the count of $0.6 erasers be `C_6`
Let the count of $0.4 erasers be `C_4`
Let the target count of `C_6` be `x`

Then no matter how many `C_4` there are the count of `C_6` must make up the difference to give a total count of 350

So the blend can be anything:

from`->" "`0 at `C_4` and 350 at `C_6 larr" condition 1"`
to`" "->`350 at `C_4` and`" "` 0 at `C_6 larr" condition 2"`

Cost at condition 1 `=350xx$0.6=$210`
Cost at condition 2`=350xx$0.4=$140`

Target value of sale `=$170.00`

So we need to blend the two sale figures in a proportion that gives $170.

The slope of part is the same as the slope of all of it.

`("change in count of "C_6)/("change in sales revenue") =350/(210-140)=x/(170-140)`

`350/70=x/30`

`x=(30xx350)/70=150" at type "C_6`

Thus we have:

count of $0.6 rubbers is 150 `larr`pumpkin erasers

count of $0.4 rubbers is `350-150=200`