The sum of two numbers is 25. One of the numbers is twice the second number plus seven. What are the two numbers?

Question

I'm learning Alegbra 1 and I need step by step to show my work on the assignment. Please and thank you.

Answer 1

since sum of two numbers is 25, then second number is 25 -x

one number is twice the second number plus 7.

let 25 - x be "one number" and x be the "second number"

25 - x = 2x + 7

18 = 3x

x = 6

other number is 25 - 6 = 19

Answer 2

Let a = the first number and let b = the second.

a + b = 25

a = 2b + 7

I see two simple ways to solve.

1. Since the second equation is already solved for one of the variables, substitute 2b + 7 for a in the first equation.

2b + 7 + b = 25

3b + 7 = 25

3b + 7 - 7 = 25 - 7

3b = 18

3b/3 = 18/3

b = 6

Substitue 6 for b in either equation.

a + 6 = 25

a + 6 - 6 = 25 - 6

a = 19

19 and 6

2. Solve the first equation for a.

a + b = 25

a + b - b = 25 - b

a = 25 - b

Now, you have two "values" for a, so they must be equal!

25 - b = 2b + 7

25 - b + b = 2b + 7 + b

25 = 3b + 7

25 - 7 = 3b + 7 - 7

18 = 3b

18/3 = 3b/3

b = 6

Solve for a the same way as #1 and you should get the same answers.

Good luck!