Question

“The sum of two numbers is 17. One number is 3 less than 2/3 of the other number. What is the lesser number?”

Answer 1

Answer: B) 5

Step-by-step explanation:

The sum of two numbers is 17.

Let x and y be those numbers.

$x+y=17$

One number is 3 less than $\frac{2}{3}$ of the other number (y).

$x=\frac{2}{3}y-3$

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We end up with these two equations.

$x+y=17\\x=\frac{2}{3}y-3$

Replace x in the first equation to find y.

$x+y=17\\\frac{2}{3}y-3+y=17$

Add 3.

$\frac{2}{3}y+y=17+3$

Combine like terms.

$\frac{2+3}{3}y=20\\\frac{5}{3}y=20$

Multiply by the reciprocal of the fraction next to y.

$(\frac{3}{5} )\frac{5}{3}y=20(\frac{3}{5} )$

$y=12$

Now replace the value of y in any of the equations to find x.

$x+y=17\\x+12=17\\x=17-12\\x=5$

Therefore, between 5 and 12, 5 is the lesser number.