Answer: B) 5
Step-by-step explanation:
The sum of two numbers is 17.
Let x and y be those numbers.
[tex]x+y=17[/tex]
One number is 3 less than [tex]\frac{2}{3}[/tex] of the other number (y).
[tex]x=\frac{2}{3}y-3[/tex]
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We end up with these two equations.
[tex]x+y=17\\x=\frac{2}{3}y-3[/tex]
Replace x in the first equation to find y.
[tex]x+y=17\\\frac{2}{3}y-3+y=17[/tex]
Add 3.
[tex]\frac{2}{3}y+y=17+3[/tex]
Combine like terms.
[tex]\frac{2+3}{3}y=20\\\frac{5}{3}y=20[/tex]
Multiply by the reciprocal of the fraction next to y.
[tex](\frac{3}{5} )\frac{5}{3}y=20(\frac{3}{5} )[/tex]
[tex]y=12[/tex]
Now replace the value of y in any of the equations to find x.
[tex]x+y=17\\x+12=17\\x=17-12\\x=5[/tex]
Therefore, between 5 and 12, 5 is the lesser number.
