the larer of two numbers is 23. if three times the larger is 5 more than eight times the smaller ,find the smaller number
3x=8y+5
3(23)=8y+5
69=8y+5
64=8y
8=y
59=8y+3
To solve this problem, we'll use algebra to represent the information given. Let's assign variables to the two numbers:
Let x be the smaller number.
Let y be the larger number.
We know the larger number is 23, so y = 23.
The problem states that three times the larger number is 5 more than eight times the smaller number. We can translate this into an equation:
3y = 8x + 5
Substituting y with 23, we have:
3(23) = 8x + 5
Simplifying:
69 = 8x + 5
Next, we'll isolate the variable x to solve for the smaller number.
Subtracting 5 from both sides of the equation:
69 - 5 = 8x
64 = 8x
Dividing both sides by 8:
x = 8
Therefore, the smaller number is 8.