The sum of two numbers is 40. The larger number (x) is 1.5 times the smaller number (y). Which system of equations models this situation?

Question

asked Jun 17, 2020 52.9k views

2 Answers

Works For A Living · Answer 1 · 2020-06-23T15:06:27+0000

Answer:

$x+y=40\\x=1.5y$

Explanation:

Taking the first statement and "transcribing" it into an equation:

"The sum of two numbers is 40":

x + y = 40

Now the second statement:

"The larger number (x) is 1.5 times the smaller number (y).":

x = 1.5y

(we don't need to worry about the "larger" and "smaller" part, they are implied by the fact that one is 1.5 larger than the other)

So the system of equations is:

$x+y=40\\x=1.5y$

If you are curious: the solution of this system goes as follows:

$y=40-x\rightarrow\\x=1.5(40-x)=60-1.5x\\2.5x=60\\x = 24\rightarrow y =40-24 = 16\\x=24, y=16$