Question 1195601
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The response from the other tutor shows a good standard method for solving the problem.<br>
But the numbers in this problem allow for a somewhat different solution method that some students might (or might not!) find easier.<br>
If x and y are the lengths of the first and second parts of the journey respectively, then we have two equations:<br>
{{{x/4+y/3=110}}}
{{{x/3+y/4=100}}}<br>
Multiply both equations by the least common denominator, 3*4=12:<br>
{{{3x+4y=1320}}} [1]
{{{4x+3y=1200}}} [2]<br>
Now, instead of using the standard algebraic method of solving the pair of equation using elimination, let's add these last two equations and simplify:<br>
{{{7x+7y=2520}}}
{{{x+y=2520/7}}}
{{{x+y=360}}}<br>
Now use this equation with equations [1] and [2] to solve the problem.<br>
{{{3x+3y=1080}}} [3]
{{{3x+4y=1320}}} [1]<br>
Subtract [3] from [1]:<br>
{{{y=240}}}<br>
{{{3x+3y=1080}}} [3]
{{{4x+3y=1200}}} [2]<br>
Subtract [3] from [2]:<br>
{{{x=120}}}<br>
Obviously we get the same answers -- by a different path.<br>
ANSWERS: The first part of the journey is x=120cm; the second part is y=240cm.<br>
CHECK:
x/4+y/3 = 120/4+240/3 = 30+80 = 110
x/3+y/4 = 120/3+240/4 = 40+60 = 100<br>