Question 1205950
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As you can see from the responses from the other tutors, there are many ways the problem can be set up for solving.<br>
I note that in all three of the solutions you have received, the tutors use some form of the equation "black=(3/4)red".  That fraction slows down the work of solving the problem.<br>
A setup that seems easier to me is this:<br>
yellow = 1 3/4 = 7/4
black = 3x
red = 4x<br>
With those expressions for the lengths of black and red, it will always be true that the length of black is 3/4 the length of red.  Now the equation that says the total length is 7m is easy:<br>
{{{3x+4x+7/4=7}}}
{{{7x=7-7/4=28/4-7/4=21/4}}}
{{{x=(21/4)/7=3/4}}}<br>
ANSWER: The length that was painted black is 3x = 9/4 m, or 2.25m<br>