the greater of two numbers is 1 more than twice the smaller. three times the greater exceeds 5 ties the smaller by 10. find the numbers and write the equation.
please help me
Let's denote the smaller number as 'x' and the greater number as 'y'.
According to the given information, we have two equations:
1. "The greater of two numbers is 1 more than twice the smaller."
This can be expressed as: y = 2x + 1
2. "Three times the greater exceeds 5 times the smaller by 10."
This can be expressed as: 3y = 5x + 10
To find the numbers, we can solve these two equations simultaneously.
First, let's solve for 'y' in terms of 'x' from equation 1:
y = 2x + 1
Next, we substitute this expression for 'y' into equation 2:
3(2x + 1) = 5x + 10
Simplifying the equation, we get:
6x + 3 = 5x + 10
Now, bring the terms involving 'x' to one side of the equation and the constant terms to the other side:
6x - 5x = 10 - 3
x = 7
Substituting the value of 'x' back into equation 1, we can find 'y':
y = 2(7) + 1
y = 14 + 1
y = 15
Therefore, the smaller number is 7 and the greater number is 15.