Question 1205318: Siti has RM450000 in her ASB. She wants to invest in Gading Mutual deposit, Maju
Makmur bar gold, Indah certificate deposit and Selamat Maju bar gold which pay
simple annual interest of 9%, 6%, 10% and 15%, respectively. Moreover, she wants
to combine annual return of 8% and want to have only one-third of investment in
Indah certificate deposit and Selamat Maju bar gold.
a. Write the linear model system equation for the whole investment.
c. Use elimination method to find each of the investment
3. Alia rows a boat upstream from one point on a river to another point 4 km away in 1.5 hours.
The return trip, traveling with the current, takes only 45 min.
a. Identify the variables involve in algebra.
b. Find the speed of the current flowing by using back-substitution method
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'll do number 3 for you.
you can then resubmit for the first one in a separate request.
if i can, i'll solve that one as well, but i'm not sure i can do it, at this time.
i do have one question on the first part.
did you mean that one third of the investment should be in indah and one third of the investment should be in selamat, or did you mean that one third of the investment should be in the sum of (indah and selamat).
. Alia rows a boat upstream from one point on a river to another point 4 km away in 1.5 hours.
The return trip, traveling with the current, takes only 45 min.
a. Identify the variables involve in algebra.
b. Find the speed of the current flowing by using back-substitution method
the formula i normally use with these is (rate of boat plus or minus rate of current) * time = distance.
let r = rate of the boat, c = rate of the current, t = time, d = distance.
formula becomes (r +/- c) * t = d
going upstream, the formula becomes (r - c) * 1.5 = 4
going downstream, the formula becomes (r + c) * .75 = 4
the time is in hours.
the distance is in kilometers.
the back substitution says solve for one of the variables and use the value of that to solve for the other variable.
your two equations to solve simultaneously are:
(r - c) * 1.5 = 4
(r + c) * .75 = 4
we'll solve for c first.
simplify both equations to get:
1.5 * r - 1.5 * c = 4
.75 * r + .75 * c = 4
in the second equation, solve for c to get:
c = (4 - .75 * r) / .75
in the first equation, replace c with that to get:
1.5 * r - 1.5 * c = 4 becomes:
1.5 * r - 1.5 * (4 - .75 * r) / .75 = 4
multiply both sides of the equation by .75 to get:
1.5 * .75 * r - 1.5 * (4 - .75 * r) = 4 * .75
simplify to get:
1.125 * r - 6 + 1.125 * r = 3
combine like terms to get:
2.25 * r - 6 = 3
add 6 to both sides of the equation to get"
2.25 * r = 9
solve for r to get:
r = 4
go back to your original equations and replace r with 4 to get:
(r - c) * 1.5 = 4 becomes (4 - c) * 1.5 = 4
(r + c) * .75 = 4 becomes (4 + c) * .75 = 4
simplify each equation to get:
6 - 1.5 * c = 4
3 + .75 * c = 4
subtract 6 from both sides of the first equation and subtract 3 from both sides of the second equation to get:
-1.5 * c = -2
.75 *c = 1
solve for c in both equations to get:
c = 1.33333.....
c = 1.33333.....
you now have r = 4 and c = 1.3333....
since 1.3333..... is the same as 4/3, you now have:
r = 4 and c = 4/3.
confirm by replacing r with 4 and c with 4/3 in the original two equations to get:
(r - c) * 1.5 = 4 becomes (4 - 4/3) * 1.5 = 4
(r + c) * .75 = 4 becomes (4 + 4/3) * .75 = 4
simplify to get:
8/3 * 1.5 = 4 becomes 4 = 4
16/3 * .75 = 4 becomes 4 = 4
this confirms the solution is correct.
the solution is that the rate of the current = 4/3 kilometers per hour which is the same as 1.333333.... kilometers per hour which is the same as 1.33 kilometers per hour when you round to 2 decimal places.
that should take care of number 3.
if you're happy with the solution, then resubmit your request with just the first part so somebody can take a look at that.
in the future, you should only submit one problem per request.
i believe that's in the guidelines and i have seen other tutors request the same from other students.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
For the first problem....
There is not enough information to find a unique solution. Mathematically, an infinite number of possible answers is possible; in actuality, since the numbers have to be whole numbers, the number of solutions is finite, but still large.
Write the equations in thousands of RM to make the numbers smaller and easier to work with.
450 = total investment
150 = total invested in Indah and Selamat (1/3 of the total)
300 = total invested in Gading and Maju (the other 2/3 of the total)
Let x = amount invested in Indah
Then 150-x = amount invested in Selamat
Let y = amount invested in Gading
Then 300-y = amount invested in Maju
The average return on the investments is 8%:
With no restrictions, that linear equation in two variables has an infinite number of solutions. If we limit the possible solutions to whole numbers of thousands (x and y non-negative integers), there are still a large number of solutions.
One easily seen solution is x=90 and y=0, corresponding to 90000 invested in Indah, 60000 in Selamat, 0 in Gading, and 300000 in Maju.
Checking that solution....
One other solution is x=120 and y=50, corresponding to 120000 invested in Indah, 30000 in Selamat, 50000 in Gading, and 250000 in Maju.
Checking that solution....
ANSWER: There is not enough information to find a unique solution
For the second problem....
I don't know what your definition is of the "back-substitution method"; I will solve using what I think is the easiest method.
The rate upstream, where the speed of the current is subtracting from the boat speed, is 4/1.5 = 8/3 mph.
The rate downstream, where the speed of the current is adding to the boat speed, is 4/(3/4) = 16/3 mph.
Informally, since the current speed subtracted from the boat speed is 8/3 mph and the current speed added to the boat speed is 16/3 mph, the boat speed is halfway between 8/3 and 16/3 mph, which is 12/3 mph, or 4 mph. Then the current speed is the difference between 4 and 8/3, or between 4 and 16/3, which is 4/3.
ANSWER: The speed of the current is 4/3 mph
NOTE: An informal solution as shown above uses logical reasoning. If required, a formal algebraic solution is relatively easy:
b = boat speed
c = current speed
b+c = 16/3
b-c = 8/3
Subtract the second equation from the first, eliminating b:
2c = 8/3
c = 4/3
ANSWER: the current speed is 4/3 mph
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