Let x1 and y1 be the two numbers of the first ratio
X(1) = 7
Y(1) = 3
Let x(2) and y(2) be the two numbers of the second ratio. Let z be the common factor
X(2) = 7z
Y(2) = 3z
Equation:
X(2) + Y(2) = 150
Substitute the given values
[tex]7z + 3z = 150 \\ 10z = 150 \\ \frac{10z}{10} = \frac{150}{10} \\ z = 15[/tex]
Substitute z to the values of the second ratio
[tex]x = 7(15) \\ x = 105 \\ [/tex]
[tex]y = 3(15) \\ y = 45[/tex]
Check:
[tex]x + y = 150 \\ 105 + 45 = 150 \\ 150 = 150[/tex]
Therefore,
The two numbers are 105 and 45.
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