SOLUTION: You are building a landscape garden and want to spend no less than $3,000 and no more than $8,000. You need 35 tons of rock, each costs $60 and each tree costs $99. How many trees

Algebra.Com
Question 329629: You are building a landscape garden and want to spend no less than $3,000 and no more than $8,000. You need 35 tons of rock, each costs $60 and each tree costs $99. How many trees can you buy out of a budget of $24,000? Show your answer using inequalities.
Also want to map (6,15), what is the y-intercept.

Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
You are building a landscape garden and want to spend no less than $3,000 and no more than $8,000.
You need 35 tons of rock, each costs $60 and each tree costs $99.
Show your answer using inequalities.
Also want to map (6,15), what is the y-intercept.
---
Let # of trees be "x":
3000 <= 35*60+99x <= 8000
---
900 <= 99x <= 5900
9.09 <= x <= 59.596
---
# of trees is
between 8 and 59
====================================
How many trees can you buy out of a budget of $24,000?
35*60+99x <= 24000
99x <= 21900
x <= 221 when rounded down to a whole number
---------------------
Cheers,
Stan H.
---------------------

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x is what you want to spend.
3000 <= x <= 8000

You need 35 tons of rocks.
Each rock costs $60 and each tree costs $99.

How many trees can you buy out of a budget of $24,000?

You need 35 tons of rocks at $60 a ton.

This means that you need a total of 35 * 60 = $2100 for rocks.

If you spend $3000 on the garden, then the number of trees you can buy would be equal to $3000 - $2100 / $99 = 9.09..... which rounds out to 9 trees.

If you spend $8000 on the garden, then the number of trees you can buy would be equal to $8000 - $2100 / $99 = 59.59..... which rounds out to 59 trees.

Since you do not want to spend less than $3,000 and you do not want to spend more than $8,000 then the fact that you have a budget of $24,000 is irrelevant.

If you spend as little as $3,000, then $21,000 remains as cash available for future projects.

If you spend as much as $8,000, then $16,000 remains as cash available for future projects.

Your formula for the number of trees you can buy would be as follows:

x >= $3000
x <= $8000
budget = $24000
rocks = $60 * 35 = 2100
trees = (x - 2100) / 99 truncated to the nearest integer that is less than that value.

You can graph this as follows:



On this graph, the value of x is given in thousands.

3 = 3000
8 = 8000

The value of y is the numnber of trees you can buy.

I set y = 9 and y = 59 to show you that these values occur at around x = 3 and x = 8

This means that when x = 3000, 9 trees can be bought.

this also means that when x = 8000, 59 trees can be bought.

You can plot the number of tree you can buy in between by looking at the graph or by solving the equation for any value of x between 3000 and 8000.

The equation used to solve is:

y = (x-2100)/99 truncated to the nearest integer smaller than or equal to y.

For example:

When x = 5000, the equation becomes:

y = (5000 - 2100) / 99 = 29.29..... which truncates to 29.

Look on the graph and you will see that when y = 29, the value of x is somewhere around 5.

Here's the graph again, with the value of y = 29 shown.



In these graphs, the value of x below 3 and above 8 are irrelevant and not to be considered.

The equation for how much money is left in the budget would be:

y = $24000 - x.

In this case y would equal the money that is left in the budget.

The graph for the money that is left in the budget is shown below:



In this graph, y represents the amount of money that is left in the budget in thousands of dollars.

$24,000 equals 24 on the graph

In this graph, x represents the amount of money that is spent on the project in thousands of dollars.

$3000 = 3 on the graph
$8000 = 8 on the graph.

The only values of x that are relevant would be the values of x from 3 to 8.

You can see that when x = 3, y = 21 which means that $21,000 is left in the budget after $3000 was spent.

You can also see that when x = 8, y = 16 which means that $16,000 is left in the budget after $8000 was spent.



RELATED QUESTIONS

you are planning to spend no less than $6,000 and no more than $10,000 on your landscape... (answered by solver91311)
Landscape Design Landscape designers often use coordinate geometry and algebra as they (answered by richard1234)
You are planning to spend no less than $6,000 and no more than $10,000 on your... (answered by mananth)
I. I want to spend no less than $3,000 and no more than $7000 on my landscaping project. (answered by rfer)
cupcakes are $4 and hot dogs are $3 each. you want to buy at least 5 items. you want to... (answered by ikleyn)
You are planning to spend no less than $6000 and no more than $10,000 on your landscaping (answered by mangopeeler07)
Can I please Have help with this, Thank You! Write the inequalities and describe the... (answered by ikleyn)
Hello, Can someone please help me to understand this problem? Thanks 1. You are... (answered by rfer)
Hello, Can someone please help me to understand this problem? Thanks 1. You are... (answered by mananth)