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Eggs. The number of eggs eaten by an average Amer…

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Problem 83 Hard Difficulty

Landscaping. A developer is going to purchase $x$ trees and $y$ shrubs to landscape a new office complex. The trees cost $\$ 50$ each and the shrubs cost $\$ 25$ each. His budget is $\$ 5,000$. This situation is modeled by the equation $50 x+25 y=5,000$. Use the intercept method to graph it.
a. What information is given by the $y$ -intercept?
b. What information is given by the $x$ -intercept?

Answer

a. If only shrubs are purchased, he can buy 200
b. If only trees are purchased, he can buy 100

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 3

Intercepts

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Video Transcript

So for this one, if we want to use the intercept method to graph it, basically what that means is we want to plug in zero for the X. The knock is those 50 times zero plus 25 y is equal to 5000 and that's what's gonna allow us to find out what our wise. So then, from here, 25 wise Eagle to 5000 and we just have to divide both sides of the equation by 25 to get that Y is equal to 200. So now we know that we have the hornet 0.0 comma 200 since we plugged in the zero for the X and got a 200 for the wine. And then if we have the same process, But we put in a zero for the why that gets rid of this component. So 50 X is equal to 5000. So then, if we divide both sides of the equation by 50 we should find out that X is equal to 100 giving us the 0.100 comma zero because we got the X coordinate what 100 when we pulled in his year of for the why. So from here I can graph it because I have 100 common. Zero is Let's call that here and you're a comma. 200 is up here so I can see that my graph is gonna look something like this. So then, in terms of the information that's given by the Y intercept when the X zero, it tells us from the graph that the trees cost $50 each and the shrubs cost $25 each. So then what that means is that we have to figure out what the X and glide values mean. Basically it. So when we have the y intercept, that means that we didn't have any exes, which means that we had no trees and we had all shrubs using his $5000 budget and then for the X intercept of 100 common zero. That means we didn't have any wise, which means no troubles. And we had all trees using his $5000 But

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