Question #a72e1

2 Answers
Feb 17, 2018

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

Feb 17, 2018

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