the larger of two numbers is 1 more than twice the smaller. three times the larger number is 10 more than 5 times the small. find both numbers.
Let s = smaller and L = Larger
L = 2s+1
3L = 5s+10
Substitute 2s+1 for L in second equation and solve for s. Insert that value into the first equation and solve for L. Check by inserting both values into the second equation.
To solve this problem, let's assign variables to represent the two numbers. Let's say the smaller number is "x," and the larger number is "y."
According to the given information:
1. "The larger of two numbers is 1 more than twice the smaller." This can be written as: y = 2x + 1.
2. "Three times the larger number is 10 more than 5 times the smaller." This can be written as: 3y = 5x + 10.
Now we have a system of two equations:
y = 2x + 1 (Equation 1)
3y = 5x + 10 (Equation 2)
We can solve this system of equations by substituting Equation 1 into Equation 2. Let's do that:
3(2x + 1) = 5x + 10
6x + 3 = 5x + 10
6x - 5x = 10 - 3
x = 7
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
y = 2(7) + 1
y = 14 + 1
y = 15
So, the two numbers are x = 7 and y = 15.