Question 1205318
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For the first problem....<br>
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.<br>
Write the equations in thousands of RM to make the numbers smaller and easier to work with.<br>
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<br>
The average return on the investments is 8%:<br>
{{{.09(y)+.06(300-y)+.10(x)+.15(150-x)=.08(450)}}}
{{{.09y+18-.06y+.10x+22.5-.15x=36}}}
{{{.09y-.06y+.10x-.15x=36-18-22.5}}}
{{{.03y-.05x=-4.5}}}
{{{.05x-.03y=4.5}}}
{{{5x-3y=450}}}<br>
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.<br>
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.<br>
Checking that solution....<br>
{{{.09(0)+.06(300)+.10(90)+.15(60)=0+18+9+9 = 36}}}<br>
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.<br>
Checking that solution....<br>
{{{.09(50)+.06(250)+.10(120)+.15(30)=4.5+15+12+4.5=36}}}<br>
ANSWER: There is not enough information to find a unique solution<br>
For the second problem....<br>
I don't know what your definition is of the "back-substitution method"; I will solve using what I think is the easiest method.<br>
The rate upstream, where the speed of the current is subtracting from the boat speed, is 4/1.5 = 8/3 mph.<br>
The rate downstream, where the speed of the current is adding to the boat speed, is 4/(3/4) = 16/3 mph.<br>
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.<br>
ANSWER: The speed of the current is 4/3 mph<br>
NOTE: An informal solution as shown above uses logical reasoning.  If required, a formal algebraic solution is relatively easy:<br>
b = boat speed
c = current speed<br>
b+c = 16/3
b-c = 8/3<br>
Subtract the second equation from the first, eliminating b:<br>
2c = 8/3
c = 4/3<br>
ANSWER: the current speed is 4/3 mph<br>