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?”

A. 7
B. 5
C. 12
D. 3

Answer 1

Answer: B) 5

Explanation:

The sum of two numbers is 17.

Let x and y be those numbers.

`x+y=17`

One number is 3 less than
`(2)/(3)` of the other number (y).

`x=(2)/(3)y-3`

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We end up with these two equations.

`x+y=17\\x=(2)/(3)y-3`

Replace x in the first equation to find y.

`x+y=17\\(2)/(3)y-3+y=17`

Add 3.

`(2)/(3)y+y=17+3`

Combine like terms.

`(2+3)/(3)y=20\\(5)/(3)y=20`

Multiply by the reciprocal of the fraction next to y.

`((3)/(5) )(5)/(3)y=20((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.