Sol1602idn
Answered

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the sum of two positive number integers when divided by the smaller gives a quotient of 2 with a remainder of 9. their s is 375. find the two integers.​

Sagot :

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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