Answer:
First number =26
Second number =49
Step-by-step explanation:
Question:
The sum of two numbers is 75. The second number is 3 less than twice the first. Find the numbers.
Given:
Sum of two numbers = 75
The second number is 3 less than twice the first.
To find the numbers.
Solution:
Let the first number be = [tex]x[/tex]
Let second number be = [tex]y[/tex]
The sum equation can be given as:
[tex]x+y=75[/tex]
It is given that the second number is 3 less than twice the first.
This can be given as:
[tex]y=2x-3[/tex]
Substituting the value of [tex]y[/tex] in terms of [tex]x[/tex] in the sum equation.
[tex]x+(2x-3)=75[/tex]
Combining like terms.
[tex]3x-3=75[/tex]
Adding 3 both sides.
[tex]3x-3+3=75+3[/tex]
[tex]3x=78[/tex]
Dividing both ides by 3.
[tex]\frac{3x}{3}=\frac{78}{3}[/tex]
[tex]x=26[/tex]
Substitution [tex]x=26[/tex] in the second equation to find [tex]y[/tex].
[tex]y=2(26)-3\\y=52-3\\\therefore y=49[/tex]
Thus, first number =26 and second number =49.
