Rachel's Radical Problems
I am Rachel and I am
here to help you learn about some Algebra2 problems. I decided to teach
you about solving with variables using Linear equations, Substitution and
Word Problems. This might sound hard and like it's a large amount of
work but once you begin it, you won't want to stop......not really but hey,
you are going to have to learn it anyways. So LET'S BEGIN!!!!!
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Word Problem:
One week a business sold 40 scarves. White ones cost $4.95, and printed ones cost $7.95. In all $282 worth of scarves were sold. How many of each color were sold? w+p=40 p=40-w p=40-12 $4.95w+7.95p=282 p=28 $4.95w+$7.95(40-w)=282 -3w+318=282 -318 -3w=-36 -3w -3w w=12 |
The first variable equals w, and the second equals p. Since there were 40 scarves sold w+p has to equal 40. The white ones cost $4.95 and the printed cost $7.95. In the equation the total amount of money is $282 , this is where we begin to plug in 40-w in place of the p. Then we multiply and get our answer which is 12. Now plug the 12 into w to solve for p., you end up with 28. |
| Linear Equation: The problem is 2L+2w+628 L=6+w 2(6+w) +2w=628 2L+2(25)=86 12+w+2w=628 2L+50=86 12+3w=628 -50 3w=616 3w 2L=36 w=25 2L L=13 |
I
n this problem L=6+w, which
you plug this in to replace the L then solve. Then you multiply the
6+w by the 2 and add the the w's together which gives you 3w. Then subtract
the 12 from 628. The outcome is 616, which you divide by 3w. Then
you plug the answer into the second part of the problem which is 2L+2w+628,
to take place of the w. Then you end up with 13.
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| Substitution:
y= 5-4x (-2,3) 3x-2y=12 3x-2(5-4x)=12 3(2)-2y=12 3x-10+8x=12 6-2y=12 11x-10=12 11x=22 11x -2y=6 x=2 -2y y=-3 |
In this problem the y=5-4x
which you plug this into 3x-2y=12 to replace the Y. Then
multipy and add the variables to come up with 11x. Then divide 22 by
11 to come up with the answer 2. Plug the 2 in place of the x in the
next problem, to get 3. 
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