Question

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?

Answer 1

x + y = 40

x - 1.5y = 0

Explanation:

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Answer 2

`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`