By defining and solving systems of equations, we will see that:
a) the fraction is 40/56
d) the fraction is 15/21.
How to write the equations?
We have the fraction 5/7 and we want to write it in different ways.
a) First we want to find a number a/b such that:
a/b = 5/7
a + b = 96
This is a little system of equations, to solve this, first we can rewrite the first equation as:
7a = 5b
Now we can isolate a on the second equation:
a = 96 - b
And replace that on the other equation:
7*(96 - b) = 5b
And now we can solve this for b.
672 - 7b = 5b
672 = 5b + 7b = 12b
672/12 = b = 56
And we know that:
a = 96 - b = 96 - 56 = 40
Then the fraction is 40/56
d) This time we want the denominator to be 9 less than twice the numerator.
in a/b, a is the numerator and b is the denominator.
So this time we have:
a/b = 5/7
b = 2a - 9
We can rewrite the first equation again:
7a = 5b
And then replace the other equation in the right side:
7a = 5*(2a - 9)
And now solve this for a.
7a = 10a - 45
45 = 10a - 7a = 3a
45/3 = a = 15.
And:
b = 2a - 9 = 2*15 - 9 = 21
Then the fraction is 15/21.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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