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The first number divided by a second number, the quotient is 45. When the first number is divided by a number two larger than the second, the quotient is 27. Find the first number?

Sagot :

x = first number
y = second number

Equation A:

[tex] \frac{x}{y} = 45[/tex]    
x = 45y    

Equation B:

[tex] \frac{x}{y+2}=27 [/tex]

Substitute 45y to x in Equation B:

[tex] \frac{45y}{y+2}=27 [/tex]

45y = 27 (y + 2)
45y = 27y + 54
45y - 27y = 54
18y = 54
18y/18 = 54/18
y = 3

Substitute 3 to y in Equation A:
[tex] \frac{x}{y} =45[/tex]
[tex] \frac{x}{3} = 45[/tex]
x = (45)(3)
x = 135

The numbers are:
First number, x = 135
Second number, y = 3

ANSWER:  The first number is 135.

Check:
135/3 = 45    (Equation A)
45 = 45

135/3+2 = 27   (Equation B)
135/5 = 27
27 = 27