Answer:
The numbers are 24 and 8.
Step-by-step explanation:
1. Let´s name the numbers as follows:
x=first number
y=second number
2. As the sum of the two numbers is 32, you have the first equation:
[tex]x+y=32[/tex] (Eq.1)
3. As the quotient of the two numbers is 3, you have the second equation:
[tex]\frac{x}{y}=3[/tex] (Eq.2)
4. Solving for x on Eq.2:
[tex]x=3y (Eq.3)[/tex]
5. Replacing Eq.3 in Eq.1:
[tex]3y+y=32\\4y=32\\y=\frac{32}{4}\\y=8[/tex]
6. Replacing the value of y in Eq.3:
[tex]x=3(8)\\x=24[/tex]
Therefore the numbers are 24 and 8.
The first number is 24 and the second number is 8.
The substitution method is one of the algebraic methods to solve simultaneous linear equations.
The sum of two numbers is 32 and their quotient is 3.
Let, the first number be x and the second number be y.
The sum of the two numbers is 32.
[tex]\rm First \ number + second \ number = 32\\\\x+y=32[/tex]
And the quotient of the two numbers is 3.
[tex]\rm \dfrac{x}{y}=3[/tex]
From equation 2
[tex]\rm \dfrac{x}{y}=3\\\\x=3y[/tex]
Substitute the value of x in equation 1
[tex]\rm x+y=32\\\\3y+y=32\\\\4y=32\\\\y=\dfrac{32}{4}\\\\y=8[/tex]
Substitute the value of y in equation 2
[tex]\rm \dfrac{x}{y}=3\\\\x=3y\\\\x=3\times 8\\\\ x=24[/tex]
Hence, the first number is 24 and the second number is 8.
To know more about the substitution method click the link given below.
https://brainly.com/question/24022178
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