Please Help, I Can’t Figure These Out Listed In The Details!?
ByFor the systems of linear equations in questions 1-3
-Determine how many solutions exist
-Use either elimination or substitution to find the solutions (if any)
-Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection
1.
Walt made an extra $9000 last year from a part-time job. He invested part of the money at a 9% annual rate of interest, and the rest at an 8% annual rate of interest. At the end of the year, he made a total of $770 in interest. How much was invested at 8%?
2.
An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.
3.
Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
3 Comments
February 8th, 2010 at 11:52 am
So these are obviously homework questions so I’m not going to answer them completely however I can help.
1.We need to figure out what percentage of the money Walt invested at 9% and what percentage at 8%. So first we must calculate the total interest earned given that x is invested at 8%.
Total=x*8% +(9000-x)*9%
you must therefore solve
770 = x*8% +(9000-x)*9%
I’ll leave the rest for you to do yourself.
2. The though parts of these types of question are to convert them into formulas, to convert this one consider these equations definintions
t=train arrival for local train
train arrival for express train=t-1
v=velocity of local train
velocity of express train =2*v
t*v=50 miles
(t-1)*2*v=50 miles
solve for v and 2*v
3. This one can be done just by defining the two variables
n= number of nickes
d=number of dimes
you can write the equations and solve
February 8th, 2010 at 3:11 pm
For each word problem you must first set up equations. using #3 you start by making X and Y equal parts of the problem. X will stand for nickels and Y for dimes.
The first equation would be nickels and dimes worth $5.65 or in the equation you create: x +y = 5.65
Then you do the same for the rest of the problem. if dimes are doubled think of it like 2 times dimes, or for an equation 2y. The nickels were increased by 8 or x +8. the second equation would read like: 2y + (x+8) = 10.45
This should be a good start for you. Most textbooks do have information regarding substitution and elimination, usually by looking in the index.
February 8th, 2010 at 9:07 pm
1) 0.08x +(9000-x)0.09 = 770
-0.01x = 770-810
x = 40/0.01 = 4000
2)express: 2x = 50; local: y = 50
express travel @ 25mph and local travel @ 50mph
3) 5x + 10y = 565; 5(x+8)+20y = 1045 = > 5x+20y = 1005
10y = 440 => y=40
5x = 565-440 => x=25