math question ? please help?

Question

the sum of two numbers is 15. three times one of the numbers is 11 less than five times the other. find the number

Answer 1

Let x and y be the numbers.

Then
x+y=15
3x=5y-11.

Multiply the first equation by 3, and rearrange the other:
3x+3y=45
3x-5y=-11

Subtract the second equation from the first:
8y=56

So y=7, and x=15-7=8.

Answer 2

•Sum of two numbers is 15:

let: x = be the 1st no.
y = be the 2nd no.

thus, x + y =15


•three times one number (3x)
is (=)
eleven less (-11) than five times the other (5y).

•compiling, 3x = -11 + 5y.

•simplier arrangement: 11 = 5y - 3x.

•use the any method for solving two equations & two unknowns:

(1st equation) y + x = 15
(2nd equation) 5y - 3x = 11

•better way is by substitution:

(1st equation yields): y = 15 - x

(subtstituting this to the value of y in the 2nd eq. yields):

(2nd eq) 5y - 3x = 11 , use: y = 15 -x

5(15 - x) - 3x = 11
75 - 5x - 3x = 11
75 - 8x = 11
75 - 11 = 8x
64 = 8x
8 = x

•and for solving y:

(use 1st equation) x + y = 15 , use x = 8
8 + y = 15
y = 15 - 8
y = 7

Answer 3

This is pretty easy, use the system of equations with

x+y=15

&

3x=5y-11

then solve for x using the first equation. x then equals x=15-y
then plug that value of x into the second equation:

3(15-y)=5y-11

after then, distribute the 3 with 15-y. You then should get

45-3y=5y-11

then, add 3y to both sides and 11 to bothe sides as well.

45-3y+3y-11=5y-11+11+3y

simplify

45-11=5y+3y

then combine like terms

56=8y

solve for y: y=7 then recall the equation that we had solved for x
x=15-y

plug in the value for y and solve for x

x=8

now we know that x=8 and y=7

but the answer we are looking for is only the value of the other number which we had referred to as "y". so the value of the other number is 7

Answer 4

You need to write two equations. Call the number F and S (for first and second).

They add up to 15 so

F+S=15

Then put the other statement into an equation

3F+11=5S

(After multiplying the first one by 3 you have to add 11 because it is 11 less than 5 times the second one.)

Rewriting the first equation to solve for F you get

F = 15-S

Now substitute in the second equation


3(15-S)+11=5S
45-3S+11=5S
56=8S
S=7 which means F=8

Those two numbers satisfy both conditions, since they add up to 15 and 3x8=24, which is 11 less that 5x7=35.

Answer 5

x + y = 15 ..... 1

3x = 5y - 11

3x - 5y = - 11 .... 2

solving the two equations simultaneously we get,

3x + 3 y = 45
3x - 5y = -11

8 y = 56

y = 7

Substituting the value of y in (1) we get,

x + 7 = 15

x = 8

Answer 6

x+y=15
3x=5y-11

x=8
y=7