Answer:
183 and 192
Step-by-step explanation:
Let the larger number be x and the smaller number be y.
[tex]\frac{x+y}{y} = 2\frac{9}{y}[/tex]
Given that: [tex]x + y = 375[/tex]
So,
[tex]\frac{375}{y} = 2\frac{9}{y}[/tex]
Change 2 and 9/y into an improper fraction
[tex]\frac{375}{y} = \frac{2y+9}{y}[/tex]
Cross multiply
[tex]2y^2 + 9y = 375y[/tex]
[tex]2y^2 - 366y = 0[/tex]
Divide both sides by 2
[tex]y^2 - 183y = 0[/tex]
[tex]y(y-183) = 0[/tex]
y = 0, y = 183
0 cannot be the answer because it doesn't satisfy the equation.
∴ y = 183
Now, lets find x (larger number)
x + y = 375
Substitute the value of y
x + 183 = 375
x = 375 - 183 = 192
Checking:
[tex]\frac{183+192}{183} = \frac{375}{183} = 2[/tex] r. 9
183 + 192 = 375
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