Bussiness and Finance Algebra question?

Question

Business and finance. Linda Williams has just begun a nursery business and
seeks your advice. She has limited funds to spend and wants to stock two kinds of
fruit-bearing plants. She lives in the northeastern part of Texas and thinks that
blueberry bushes and peach trees would sell well there. Linda can buy blueberry
bushes from a supplier for $2.50 each and young peach trees for $5.50 each. She
wants to know what combination she should buy and keep her outlay to $500 or
less. Write an inequality and draw a graph to depict what combinations of blueberry
bushes and peach trees she can buy for the amount of money she has. Explain the graph and her options.

Need answer asap, thanks

Answer 1

Linda wants to spend no more than $500 on trees and bushes. She's going to buy a certain amount of blueberry bushes (we don't know how many, so let's call that number b) and peach trees (we'll call that p).

All you can do at this point is to figure out how much each bunch of trees or bushes will cost. She's going to spend 2.5b on blueberry bushes and 5.5p on peach trees. So an inequality for this could be:

2.5b + 5.5p <= 500

If we were to rewrite in terms of peach trees, we'd have:

2.5b + 5.5p <= 500
5.5p <= 500 - 2.5b
p <= 1000/11 - 5b/11

You can graph this on an x-y coordinate plane if you use b for the x-axis and p for the y-axis. You'll end up with a line sloping downward, starting from about 90.9 on the p-axis (y-axis) and going down toward 200 on the b-axis (x-axis).

Graphically, this tells you how many peach trees you can get if you know how many blueberry bushes you want - simply read off the number of blueberry bushes you want and stay under your sloped line to read off how many peach trees you can afford to get. The inequality above can give you a more precise answer. If you want all blueberry bushes, for example, you'd want 200 - you'd spend $500 total for them. Or, if you want all peach trees, you'd have to get 90 - you'd spend $495 on them. If you wanted, say, 100 blueberry bushes, plug it in to your inequality:

p <= 1000/11 - 5b/11
p <= 1000/11 - 5(100)/11
p <= 1000/11 - 500/11
p <= 45

So you can get at most 45 peach trees with your 100 blueberry bushes and still spend less than $500.