The larger of two numbers is 15 more than the smaller number. Five times the larger number is 40 more than twelve times the smaller number. Find the numbers.

10, 20

Step-by-step explanation:

x = larger number

y = smaller number

...

x = 10+y

5x=40+6y

...

Substitution of x into the second equation

5(10+y)=40+6y

50 + 5y = 40 + 6y

...

Isolate y

5y - 6y = 40 - 50

-y = -10

Divide both sides by -1

y=10 is the smaller number

...

Rearrange x = 10+y to y = x-10

Substitute into 5x=40+6y

5x = 40 + 6(x-10)

5x = 40 + 6x - 60

...

Isolate x

5x - 6x = 40 - 60

-x = -20

Divide both sides by -1

X=20 is the larger number

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since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)