The sum of two numbers is 17 . One number is 3 less than (2)/(3) of the other number. What is the lesser number? 12 7 5 3 My Progress Comerance

Define Variables: Let x be the larger number and y be the smaller number. The sum of the two numbers is given as 17. So, we write the equation: x + y = 17 Express Relationship: It's also given that one number is 3 less than two-thirds of the other number. We can express this relationship as: y = (2/3)x - 3 Substitute and Simplify: Substitute the expression for y from the second equation into the first equation: x + (2/3)x - 3 = 17 Combine Like Terms: Combine like terms: (5/3)x - 3 = 17 Isolate x: Solve for x by first adding 3 to both sides: (5/3)x = 20 Find y: Multiply both sides by 3/5 to isolate x: x = (3/5) * 20 x = 12 Final Solution: Substitute x = 12 back into the equation for y: y = (2/3)*12 - 3 y = 8 - 3 y = 5

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The sum of two numbers is 17 . One number is 3 less than
(2)/(3) of the other number. What is the lesser number?
12
7
5
3
My Progress
Comerance

The sum of two numbers is $17$ . One number is $3$ less than $\frac{2}{3}$ of the other number. What is the lesser number? $\newline$ $12$ $\newline$ $7$ $\newline$ $5$ $\newline$ $3$ $\newline$

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Full solution

Q. The sum of two numbers is

17

. One number is

3

less than

\frac{2}{3}

of the other number. What is the lesser number?

\newline

12

\newline

7

\newline

5

\newline

3

\newline

Define Variables: Let $x$ be the larger number and $y$ be the smaller number. The sum of the two numbers is given as $17$ . So, we write the equation: $\newline$ $x + y = 17$
Express Relationship: It's also given that one number is $3$ less than two-thirds of the other number. We can express this relationship as: $y = \frac{2}{3}x - 3$
Substitute and Simplify: Substitute the expression for $y$ from the second equation into the first equation: $\newline$ $x + \frac{2}{3}x - 3 = 17$
Combine Like Terms: Combine like terms: $\frac{5}{3}x - 3 = 17$
Isolate $x$ : Solve for $x$ by first adding $3$ to both sides: $\newline$ $(\frac{5}{3})x = 20$
Find $y$ : Multiply both sides by $\frac{3}{5}$ to isolate $x$ :
$x = \left(\frac{3}{5}\right) \times 20$
$x = 12$
Final Solution: Substitute $x = 12$ back into the equation for $y$ : $y = \left(\frac{2}{3}\right)*12 - 3$ $y = 8 - 3$ $y = 5$