Question

One number is 9 more than 3 times another. If their difference is 29, what is the larger number?

22
29
35

Answer 1

39

Explanation:

`x,y-\text{numbers}\\\\\text{One number is 9 more than 3 times another:}\ x=3y+9\\\text{Their difference is equal to 29:}\ x-y=29\\\\\text{We have the system of equations}\\\\\left\{\begin{array}{ccc}x=3y+9&(1)\\x-y=29&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\(3y+9)-y=29\\3y+9-y=29\qquad\text{subtract 9 fro both sides}\\3y-y+9-9=29-9\qquad\text{combine like terms}\\2y=20\qquad\text{divide both sides by 2}\\(2y)/(2)=(20)/(2)\\y=10\\\\\text{Put it to (1):}\\x=3(10)+9\\x=30+9\\x=39`

Answer 2

39

Explanation:

x-3y=9

x-y=29

subtract

-2y=-20

y=10

x-10=29

x=39