Question

Question #a72e1

Answer 1

See explanation

Explanation:

You have two boxes and each has a mixture of apples and oranges.

After removing 12 apples from one box you are left with a number of apples and 10 oranges. This box is priced at $30

After removing 2 oranges from the other box you are left with a number of oranges and 6 apples. This box is priced at $12.

What is the cost of 1 apple and 1 orange?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

At those prices I am glad I do not shop there!

Answer 2

Write the given equations as
`y = mx + b`

Explanation:

One way to come up with word problems for these equations is to make them into linear functions   `y = mx + b`

`-12x + 10y = 30`   Solve for `y`

1) Add `12x` to both sides to isolate the `10y` term
`10y = 12x + 30`

2) Divide all the terms on both sides by `10` to isolate `y`
`y = 1.2x + 3`

This equation states that
The "total" (total cost or total whatever, which is `y` )
... is calculated by
1) first multiplying `1.2` times `x` (each item)
2) then adding a flat amount of `3` (which is `b` )

So here is a possible word problem:

The Adventure Restaurant has a rock-climbing activity for children.

The restaurant charges each child $1.20 per hour plus a one-time equipment fee of $3 to climb up a rock face.

Question

How much money did the restaurant take in when a birthday party of `10` children spent an hour climbing the rock face?

`y =  1.2x +   3`
`10y = 12.0x + 30`

`10y = $12` (for `10` one-hour climbs) `+ $30` (for `10` kids' activity fees)

Answer
For `10` children, the restaurant collected `$42`

`color(white)(mmmmmmmm)` __ ___ ____

Given `6x-2y=12`   Solve for `y`

1) Subtract `6x` from both sides to isolate `-2y`
`- 2y = - 6x + 12`

2) Divide all the terms on both sides by `-2` to isolate `y`
`y = 3x - 6`

This result means that the total (which is `y` ) amounts to `3` times the "units" (which is `x` ), with `6` subtracted.

Caroline Randolph owns Carolina Farms, which grows heirloom vegetables for upscale CSA clients.

She expects to harvest `3` lb of heirloom carrots per plot, but she also expects to lose `6` lb overall due to moles.

Question
How many pounds of carrots will she net if she plants 20 plots?

Answer
`y = 3  x    - 6`
`y = 3(20) - 6`
`y =   60    - 6`
`y =        54`

She will net `54` lb of heirloom carrots if she plants `20` plots.

`20` plots @ `3` lb ea . . . . . . . . . . . `60` lb
Minus `6` lb eaten by moles . . . `- 6` lb
......................................................................................
Net . . . . . . . . . . . . . . . . . . . . . . . . `54` lb