Question #41282

3 Answers
Jan 8, 2018

11 and 16

Explanation:

First, write the problem in the form of a system of equations:
27 = x + y
x = 2y - 6

Next, using substitution, combine the two equations replacing x in the first equation with the value of x in the second:
27 = (2y - 6) +y

Then, simplify and solve for y:
27 = 3y - 6
33 = 3y
y = 11

Finally, plug in the value of y into the original equation and solve for x:
27 = x + 11
x = 16

You can check your values of x and y by plugging them into both original equations and determining if they fulfill it:
27 = 11 + 16
27 = 27 Check

16 = 2(11) - 6
16 = 22 - 6
16 = 16 Check

Jan 8, 2018

11" and "16

Explanation:

"let the 2 numbers be "x" and "y

"then "x+y=27color(white)(x);x>y

"larger number "x=2y-6

rArr2y-6+y=27

rArr3y-6=27

"add 6 to both sides"

rArr3y=33rArry=11

"substitute into "x+y=27

rArrx+11=27rArrx=16

Jan 8, 2018

"The numbers are " 11 and 16

Explanation:

To solve it, assumed the following variables:
Let x= the smaller number
Let y= the bigger number

Now, formulate equations that relate the assumed numbers as prescribed in the problem; hence,

x+y=27->eq.1
y=2x-6->eq.2

Then, solve the problem through substitution method; given the value of y as shown in the formulated eq.2 above. So that:

x+color(red)(y)=27, substitute the value of y

x+color(red)((2x-6))=27, simplify the equation

x+color(red)(2x-6)=27, combine like terms

3x-6=27, add 6 both sides of the equation to isolate the term with variable x.

3x-6+6=27+6, simplify and combine like terms

3x=33, divide both sides by 3

x=11

"Therefore:"

color(red)(x=11)

y=2x-6->eq.2, substitute the value of x=11

y=2(11)-6

y=22-6

color(blue)y=16

Check:
color(red)(x)+color(blue)y=27
11+16=27
27=27