Bryan has 180 feet of fencing to fence off his rectangular garden. He will use the wall of his house as one side of the garden.
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The value of numerators are 3 and 5
<em><u>Solution:</u></em>
Let the numerators of two fractions be x and y
Two fractions have denominators 4 and 6. Their sum is 19/12
Therefore,
Cross multiply L.H.S to get simplified
If the numerators are switched their sum is 7/4
Therefore,
On simplification, we get
<em><u>Solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 1 by 4</u></em>
24x + 16y = 152 --------- eqn 3
Multiply eqn 2 by 6
24x + 36y = 252 ---------- eqn 4
<em><u>Subtract eqn 3 from eqn 4</u></em>
24x + 36y = 252
24x + 16y = 152
( - ) -------------------
20y = 100
<h3>y = 5</h3><em><u>Substitute y = 5 in eqn 1</u></em>
6x + 4(5) = 38
6x = 38 - 20
6x = 18
<h3>x = 3</h3>Thus the value of numerators are 3 and 5