Eleven times one number is 9 more than 8 times another number. The first number minus four is half the second number. Enter the smaller of the two numbers.

Question

asked Sep 10, 2023 74.3k views

1 Answer

Nicholas · Answer 1 · 2023-09-15T16:20:33+0000

Let the numbers are: x and y

Eleven times one number is 9 more than 8 times another number

so,

$11x=8y+9\rightarrow(1)$

And, The first number minus four is half the second number

so,

$x-4=0.5y\rightarrow(2)$

from equation (2):

substitute with (x) into equation (1) then solve for (y):

$\begin{gathered} 11(0.5y+4)=8y+9 \\ 5.5y+44=8y+9 \\ 5.5y-8y=9-44 \\ -2.5y=-35 \\ \\ y=(-35)/(-2.5)=14 \end{gathered}$

substitute with (y) into equation (2) to find (x):

$\begin{gathered} x-4=0.5\cdot14 \\ x-4=7 \\ x=7+4 \\ x=11 \end{gathered}$

so, the answer will be:

The smaller of the two numbers = 11