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ali015
To solve this, set up two equations using the information you're given. Let's call our two numbers a and b:
1) Difference of two numbers is 90
a - b (difference of two numbers) = 90

2) The quotient of these two numbers is 10
a/b (quotient of the two numbers) = 10


Now you can solve for the two numbers.
1) Solve the second equation for one of the variables. Let's solve for a:
a/b = 10
a = 10b

2) Plug a =10b into the first equation and solve for the value of b:
a - b = 90
10b - b = 90
9b = 90
b = 10

3) Using b = 10, plug it back into one of the equations to find the value of a. I'll plug it back into the first equation:
a - b = 90
a - 10 = 90
a = 100

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Answer: The numbers are 100 and 10
Lanuel

The difference of two numbers is 90 and their quotient is 10, the numbers are 100 and 10.

  • Let the two numbers be x and y respectively.

In Mathematics, quotient simply means division, which is the division of a number by another number.

Translating the word sentence into an algebraic expression, we have;

Difference of two numbers is 90:

  • [tex]x -y=90[/tex]    ....equation 1.

Quotient of the two numbers is 10:

  • [tex]\frac{x}{y} = 10[/tex]   ....equation 2

To find the numbers:

From eqn. 1; [tex]x=10y[/tex]

Substituting eqn. 3 into eqn. 1, we have:

[tex]10y-y=90\\\\9y =90\\\\y=\frac{90}{9}[/tex]

y = 10

For the value of x:

[tex]x=10y\\\\x=10(10)[/tex]

x = 100

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