The sum of two numbers is 35. Their difference is 13. What are the two numbers?

Question

I know it's easy, but help me anyway, while your at it figure out this one too.
The difference of two numbers is 6. The second is 9 less than 2 times the first. What are the two numbers?

Please help me solve this, And the second one too, Thank you so much for your help :) No attitude here..

Answer 1

Question 1
x + y = 35
x - y = 13---ADD
2x = 48
x = 24
y = 11
Numbers are 24 and 11

Question 2
x - y = 6
y = 2x - 9

x - (2x - 9) = 6
- x + 9 = 6
x = 3
y = - 3
The numbers are 3 and - 3

Answer 2

(11,24) Let's do the second problem which will help you with the first. Suppose one number is x, then the other number is (x-6). Now translate the English into the mathematics: (x-6)=2x-9. Put the x's (unknowns) on the same side of the equation and the knowns (those expressions not containing the x's) on the other side of the equation. Equation means that both sides balance. So, if we add 9 to both sides, we get x+3=2x. See how we've simplified, and there's still a balance. Subtracting x from both sides, we get 3=x. This means that if we put in x=3 into the equation and check to see what (x-6) is we find that (x-6)=(3-6)=(-3). Translate back to English: 3-(-3)=3+3=6. Next, (x-6)=2(3)-9=6-9=(-3). Note x=3 and (x-6)=2x-9=2(3)-9=(-3). The first problem requires that m+n=35, or m=35-n. Put in for m in your second condition (equation): m-n=(35-n)-n=35-2n=13. If we add 2n to BOTH sides and subtract 13 from BOTH sides, keeping the balance we get 35-13=22=2n, and dividing BOTH sides by 2 we get 11=n and m=(35-n)=(35-11)=24. We may write the answer (solution) as (11,24).

Answer 3

Since the two numbers have a difference of 13,
take them as x and (x+13)

x+(x+13) = 35
2x+13 = 35
2x = 35-13
2x = 22
x = 11

So the numbers are 11 and (11+13)
= 11 and 24

2nd question is similar.
U have 2 numbers, the 2nd one is 9 less than 2 times the 1st. So if the 1st is x, the 2nd is (2x-9).

From there, (2x-9)-x = 6
x-9 = 6
x = 15
so the 2nd 1, (2x-9), = 2(15)-9
=30-9
=21

Your two numbers are 15 and 21

Answer 4

let the two numbers be x,y. from the problem we get the following equations x-y=22 2(x+y)=96 x+y=96/2=48 on solving those two equations we get 2x=70 x=35;y=13.

Answer 5

the first one, the #'s are 11 and 24. That one you can do just by a chart: 1 + 14, 2+ 15, etc.
the 2nd one, let x = the 1st number, and 2x-9 = the 2nd. (since it's 2 times 9 less than the first number)
then make an equation. the +6 is because the difference is 6.
x + 6 = 2x-9
x + 15 = 2x
15 = x
and then 21 = 2x -9
so your numbers are 15 and 21

Answer 6

first question: let 'x' be bigger no. and 'y' be the smaller no.

x + y = 35
x= 35-y ----Eqn 1
x - y = 13 -----Eqn 2

Substitute 1 into 2:
(35-y) - y = 13
-2y = 13 - 35
hence, y = 11
From eqn 1: x = 35 - 11 = 24


2nd question:
let 'a' be the bigger no. and 'b' be the smaller one.

a - b = 6 ----eqn1

2a is "two times the first" and so,
b = 2a - 9 ----eqn 2

substitute 1 into 2:
a - (2a - 9) = 6
a - 2a + 9 = 6
-a = 6 - 9
hence, a = 3
and b = 2(3) - 9
= -3

Answer 7

x + y = 35
x - y = 13

I'll let you actually do the work here. It isn't difficult.

Your other problem:

x - y = 6
y = 2x -9 or 2x - y = 9

Do the same thing for this system of two linear equations of two variables.

Answer 8

"while your at it figure out this one too."

With that attitude you're not going to get anyone to help you. Here's a hint: set it up as a system of equations involving x and y.

Answer 9

x+y=35
x-y=13

x=13+y

(13+y)+y=35
13+2y=35
y=11
x=24

The numbers are 11 and 24.

Answer 10

x + y = 35

x - y = 13
x = 13 + y

13 + y + y = 35
2y = 22
y = 11 therefore x = 24

------------------------------------------------------------------

x - y = 6

2x - 9 = y

x - (2x - 9) = 6
x - 2x + 9 = 6
-x + 9 = 6
x = 3
y = -3