One number is 6 more than 2 times another. Their product is 20. Find the numbers.

Question

One number is 6 more than 2 times another. Their product is 20. Find the numbers.

Answer 1

One number is 6 more than 2 times another:

x = 2y + 6

 

Their product is 20:

xy = 20

 

We have two equations:

1)  x = 2y + 6

2)  xy = 20

 

Replace x with 2y + 6 in equation 2

(2Y+6)(Y) = 20    MULTIPLY THRU TO CLEAR PARENTHESIS

2Y² + 6Y = 20      SUBTRACT 20 FROM BOTH SIDES

2Y² + 6Y - 20 = 0   FACTOR OUT 2 FROM EACH TERM

2(Y² + 3Y - 10) = 0   DIVIDE BOTH SIDES BY 2

Y² + 3Y - 10 = 0

 

We can factor this equation...

The factors of -10 that add to 3 are (5)(-2)

 

(Y+5)(Y-2) = 0

Either y+5 = 0 and y=-5

Or      y-2 = 0 and y = 2

 

If y = -5 then

x(-5) = 20

x = 20/-5

x = -4

 

Solution 1:  {-4, -5}

 

If y = 2

x(2) = 20

x = 20/2

x = 10

 

Solution 2:  {10, 2}

 

Check answers:

 

For {-4, -5}                For {10,2}

x = 2y + 6                  x = 2y+6

-4 = 2(-5)+6               10 = 2(2)+6

-4 = -10 + 6               10 = 4+6

-4 = -4                       10=10

 

xy = 20                      xy=20

(-4)(-5)=20                10(2) = 20

20=20                        20 = 20

 

Both solutions are valid.

Answer 2

hey steph, 

the first sentence is translated like this 

a number call it x

the other number call y

one number is 6 more than 2 times the other number now can be interpreted as

x=2y+6

the second sentence says the product of x and y is 20

so xy=20

now we have x=2y+6

xy=20

a system of two equations 

we can use substitution x=20/y

in the first equation we replace x by 20/y

20/y=2y+6

cross multiply 

y(2y+6)=20

2y^2+6y-20=0 simplify first 

y^2+3y-10=0

solve the quadratic equation 

(y+5)(y-2)=0

so y=-5 or y=2

there two possibilities here 

if y=2 then x=20/2=10

or y=-5 then x=20/-5=-4