The smaller number is 15 and larger number is 36.
Step-by-step explanation:
Let,
Smaller number = x
Larger number = y
According to given statement;
The sum of two numbers is 51.
x+y = 51 Eqn 1
Four times the smaller number is 24 more than the larger number.
4x = y+24
4x - 24 = y
y = 4x-24 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]x+(4x-24)=51\\x+4x-24=51\\5x=51+24\\5x=75[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{75}{5}\\x=15[/tex]
Putting x=15 in Eqn 2
[tex]y=4(15)-24\\y=60-24\\y=36[/tex]
The smaller number is 15 and larger number is 36.
Keywords: linear equation, substitution
Learn more about linear equations at:
- brainly.com/question/9720317
- brainly.com/question/9621364
#LearnwithBrainly
