Tutor profile: Sarah E.
What is a regular polygon and how do you find the angles and perimeter.
A regular polygon is a polygon where all the sides are equal length and all the angles are equal as well. You can find the angles of any given regular polygon using this formula, $$180/n$$ where $$n$$ is the number of angles in the polygon. To find the perimeter you multiply the single given length by the number of sides.
How do you find an equivalent ratio? For example, find the number that makes the ratio equivalent to $$3:5$$
A ratio is a comparison of two numbers; for example, a ratio of $$1:3$$ means that for every one object, there are three of a corresponding object. An equivalent ratio is just a multiple of the original ratio; meaning, a ratio of $$1:3$$ is equivalent to $$2:9$$ and $$3:9$$. To find a ratio that is equivalent to a given ratio, you just have to multiply the given ratio by any number. So, an equivalent ratio to $$3:5$$ can be $$6:10$$ or $$9:15$$ etc.
How do you set up a system of equations and solve for x and y? For example, the admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
To set up a system of equations you have to read through the word problem and select important data. For the example, you have given we have... $1.50 per child (Let X=children attended) $4.00 per adult (Let Y=adults attended) 2200 people entered the fair and $5050 was earned. We can create the first equation using the costs per child, per adult, and the amount earned. $$1.50X+4Y=5050$$ This is read as the children's fee times the amount of children added to the adult fee times the amount of adults is equal to the total earned for the day. The next equation would be simply $$X+Y=2200$$ This is just the amount of children added to the number of adults equal to the total amount of people attended. Now we have the system, $$1.50X+4Y=5050$$ $$X+Y=2200$$ In $$X+Y=2200$$, we can solve for either $$X$$ or $$Y$$. Let's solve for $$Y$$ $$X+Y=2200$$ subtract $$X$$ from both sides $$Y=2200-X$$ Now that we have $$Y$$, we can plug it into the other equation, $$1.50X+4Y=5050$$ $$1.50X+4(2200-X)=5050$$ Distribute the $$4$$ $$1.50X+8800-4X=5050$$ Now we can solve for $$X$$ by combining the coefficients of the $$X$$'s and subtracting $$8800$$ from both sides. $$1.50X+8800-4X=5050$$ $$-2.5X=-3750$$ Then divide by $$-2.5$$ $$X=1500$$ So now that we have $$X$$, we can plug this into the original equation and find $$Y$$. $$Y=2200-X$$ $$Y=2200-(1500)$$ $$Y=700$$ Therefore there were $$1500$$ children who attended and $$700$$ adults.
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