Question

The sum of 5 times one number, x, and 4 times a second number, y, is 75. If the sum of the two numbers is 18, find the two numbers.


Enter a system of equations to represent the situation, then solve the system.

Answer 1

Answer:$x=3$ and $y=15$

Step-by-step explanation:

First, we are told "sum of 5 times one number, x, and 4 times a second number, y, is 75":

$5x+4y=75$ (1)

Then, we are told "he sum of the two numbers is 18":

$x+y=18$ (2)

At this point we have our system of equations and now we are able to find the values of $x$ and $y$.

So, let's begin by isolating $x$ from (2):

$x=18-y$ (3)

Substituting (3) in (1):

$5(18-y)+4y=75$ (4)

Finding $y$:

$90-5y+4y=75$

$y=15$ (5) This is the value of $y$

Substituting (5) in (1):

$5x+4(15)=75$ (6)

Finding $y$:

$5x+60=75$ (7)

$x=3$ (8) This is the value of $x$