Question 470280
<br> Wow! How about pasting the whole exam paper into one question? I believe your chances of getting an answer to your question will greatly improve if you decide to post questions one by one. Anyway, here are the answers for your first question. Answers to your second question will be very difficult to figure out without the graph of the backyard.<br>
1.a. 
The main trick here is to define a variable, say m, to stand for "the money I am willing to spend on the project". The rest is simple:
$6,000 <= m <= $10,000.
The only thing to ponder for a second are the symbols <=. Should they both be <= or should one of them be <, or should they both be <. Always check these details since the formulation of these types of sentences in English can be sometimes quite tricky. An easy way to figure this out is asking yourself questions like: "Is $6,000 acceptable according to the sentence given?" If yes, then symbol <= is fine there. If not but anything else greater than $6,000 is, then you need to use < symbol instead of <=. The same way with the other edge. "Is $10,000 acceptable?" If yes, <= symbol should be fine. Here, both symbols should indeed be <=.<br>
1.b. 
This is about money. Budget is $2500. So whatever you need to buy the total must be less than or equal to $2500. In other words, "bunch of staff <= $2500". So, what is this "bunch of stuff" for us? Apparently, rocks and trees. In particular we need 30 tons of rock while each ton is $60. This will cost us 30*$60 = $1800. Then we want some trees, with each tree being priced at $84. We do not know how many trees to buy but we know that:
$1800 + $84*T <= $2500
Simplifying this inequality, we can get:
$84*T <= $700, 
from where we have:
T <= 8.3333...
Hence the maximum number of trees you can buy is 8 (Assuming you cannot buy 1/3 of a tree for a third of a price).<br>
1.c. 
Yes, 5 trees would be a solution to the above inequality since substituting T = 5 into the inequality T < 8.333... does not invalidate the inequality.<br>