Algebra Geometry
How to Use Algebra to Plan Your Future
By Ann Knapp
Algebra represents some peoples' fondest memories of high school-and for others, it goes down in personal history as the one activity that tuned them out on math forever. But algebra offers instant help with an issue nearly everyone needs to think about-personal finances. For an example, let's use algebra to figure the age at which you should begin withdrawing Social Security.
Social security remains a popular-yet always-controversial-government program. When President Franklin Delano Roosevelt created it during the Great Depression, critics accused him of moving the country toward socialism. Today, though it remains a surefire issue with voters, it's also perennially up for reform. Policy experts propose abolishing it, turning part of it over to private investment, raising the retirement age required to collect it, reducing some Americans' eligibility for it, or simply leaving it alone.
But in any case, despite gloomy predictions of a few years ago, it looks like Social Security will be around for awhile. That means most of us need to think about when to start collecting benefits-age 62 or 66.
After all, according to current law, you (or your grandpa) will be eligible for benefits by the age of sixty-two. But that monthly check will get bigger if you wait until age sixty-six to start withdrawing from the system to which you've been contributing during your entire working life. Perhaps, thinking of your grandchildren, you'd like to know how long you'll have to live to make it more profitable to wait until age sixty-six to start taking payments. (For much of this information, by the way, the author is indebted to the PUMAS [Practical Uses of Math and Science] home page, maintained by NASA and the California Institute of Technology.)
If you've been studying your algebra, however, you can figure this problem simply. If you begin collecting social security at age sixty-two, the amount you can draw will be reduced by twenty percent (20%). So simply turn the problem into an equation. Let a represent your age and b your social security income per year. If you retire at age sixty-two, because of that twenty percent penalty, your total earnings in any given year can be represented like this: 0.8b (a-62). (By the way, if you've already forgotten your algebra, simply remember that 0.8b is another way of saying "0.8 times b"; putting the whole shebang next to another number in parentheses-as we've done here-simply means that you multiply the number within the parentheses by the 0.8b.)
Why the 0.8 times b? Because, given that twenty percent penalty, you'll get only eighty percent of b (100%-20%=80%), and 0.8 times any number yields eighty percent of that number. So, if you begin withdrawing at age sixty-two, it's 0.8b (a-62), with a indicating, again, your age.
Meanwhile, if you wait until age sixty-six to begin drawing your benefits, your equation looks like this: b(a-65). In other words, b times your age minus sixty-five.
So, to find out at what age things even out-the age that, if you live past it, it becomes more profitable to start withdrawing social security money at age sixty-five-you posit that these two equations are equal to each other, and you solve from there:
0.8b(a-62) = b(a-65)
Anyone who remembers middle-school algebra knows the first step to take: simplify the equation by dividing y from both sides. That gives us 0.8(a-62) = a-65.
If we then solve for a, we find ourselves with the solution 77. In other words, if you (or grandpa) think you can live past age seventy-seven, then at that point the earnings you get by waiting until you're sixty-five surpass the earnings you'd get by beginning at sixty-two. So you're better off waiting until you're sixty-five to begin withdrawing that social security money.
But these equations aren't just useful for people who are figuring their future social security income. Algebra is useful for young children whose parents may decide to apply the same delayed-gratification logic to their allowances. Let's say that your parents decide that you can have twenty dollars a week now-or thirty dollars a week if you can wait until a year from now, while the money they would've given you sits in a savings account. Do the math!
Algebra/geometry?
Do you ever use Algebra/geometry in college once you are out of high school??
I use it everyday at work…yes it is important
Algebra & Geometry?
i’m getting like a B- in algebra 1 and i was wondering if i should do honors or grade-level geometry next year, since everyone says they’re so different. i’m basically a B student in math and an A student in everything else
memorizing stuff i can do. im not sure what u mean by “spatial skills”, though
memorizing stuff i can do. im not sure what u mean by “spatial skills”, though
Honors Geometry has the same Algebra in it that regular geometry has. The big difference is that honors geo will have more proofs which are long problems where you prove that something must be true based on given information. This is the most frustrating part about geo classes for most students.
Proofs are like logic problems or crossword puzzles. They seem difficult or impossible at first, but as you work on them you really begin to piece things together. If this sounds like fun, then you’ll really enjoy geometry. If not, you may struggle.
I recommend that with your teacher’s and parent’s approval, you try honors. It’s easy to step down to regular geo during the year of it’s too hard, but impossible to go up to honors from regular during the year.
Good luck this year and next!
Algebra/Geometry?
Do you ever use Algebra/Geometry in college once you are out of high school??
You will use Algebra because you need to pass some Math classes. How much algebra you will depends on your Major, but expect to use it if you have plans to get a college degree.
x
x + 1
x + 2
x + 3
x + 4
those are five consecutive numbers. To find the means add all the numbers and divide by how many numbers thereare, which in this case, 5.
(x + x + 1 + x + 2 + x + 3 + x + 4) / 5 = 55
5x + 10 = 275
5x = 265
x = 53
the five numbers are 53, 54, 55, 56, and 57
algebra/geometry???
i’m homeschooled.i never took the second half of algebra2 or the whole year of algebra 1. i’m doing geometry(10th grade stuff) but i’m in the 9th grade because i changed schools and my old schools 7th & 8h grade stuff was harder than the my new schools ninth grade stuff(i was homeschooled 7-9th gd). i like 60% understand geometry but i always get majority of the questions right if explained properly in the book .do you think when i go back to regular school I’ll be screwed and be dumb or do you think i’ll do just fine?I’ll be taking 10th grade geometry when I do.but i skipped a grade so rite now i’m supposed to be in 8th but i’m in 9th but i take 10th grade math becuz my new curriculum is mad easy(for me anyways)
i mean i understand geometry like 50% actually but i need a to reread back on the pages. to get it. also do they give you chart so u can reread the postulates during a test or do u have 2 remember them by heart
I think if your starting your new school at the begining of the school year then you will be fine. Trust me, I have struggling in math the whole time I was in school and I made it through just fine and moved on to college and college level math. If you stay on track with your class than you should have no problem. And I’m sure your school offers some tutoring so if you need extra help thats a great way to do it. Tutoring helps more than you think. Good luck!
Algebra – geometry?
The mean of 5 consecutive integers is 55. What are the integers?