40. The greater of two numbers is 1 ore than twice the smaller. Three times the greater exceeds 5 times the smaller by 10. Find the numbers.

How do i start please explain. WHere do i start and how to do do this. AM very confused.

G=1+2S

3G-10=5S

check those statements.

k thx got it

G = 1 + 2 S

3 G - 10 = 5 S

3 ( 1 + 2 S ) - 10 = 5 S

3 + 6 S - 10 = 5 S

6 S - 5 S = 10 - 3

S = 7

G = 1 + 2 S

G = 1 + 2 7

G = 1 + 14

G = 15

G = greater number

S = smaller number

To solve this problem, you can approach it by setting up a system of equations based on the given information.

Let's assume that the smaller number is represented by x, and the larger number is represented by y.

According to the first statement, "The greater of two numbers is 1 more than twice the smaller," we can translate this information into an equation:

y = 2x + 1 (Equation 1)

The second statement states, "Three times the greater exceeds 5 times the smaller by 10." We can also translate this into an equation:

3y = 5x + 10 (Equation 2)

Now, you have a system of equations (Equation 1 and Equation 2) that you can solve simultaneously to obtain the values of x and y.

To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution as an example.

1. Since Equation 1 gives y in terms of x, we can substitute the expression 2x + 1 for y in Equation 2:

3(2x + 1) = 5x + 10

2. Simplify the equation:

6x + 3 = 5x + 10

3. Move all the terms involving x to the left side and the constant terms to the right side:

6x - 5x = 10 - 3

x = 7

4. Now substitute the value of x back into Equation 1 to solve for y:

y = 2(7) + 1

y = 14 + 1

y = 15

Therefore, the smaller number (x) is 7, and the larger number (y) is 15.