Question

Q. Three times a number added to a second number is 33. The first number added to three times

the second number is 19. Find the two numbers.


A. X=3 and y=3
B. X=7 and y=0
C. X=10 and y=3
D. X=5 and Y=-3

Answer 1

C. X=10 and y=3

Explanation:

Let's start by saying the first number is x and the second number is y. Now, rewrite the word problem, making sure any numbers in written form are in number form:

• 3 times x added to y is 33. x added to 3 times y is 19.

Now, translate the operations into how we usually see them in equations, e.g. "added to" as +:

`3x + y = 33`

`x + 3y = 19`

From here on, it's just solving systems of equations, baby!

• Multiply one of the equations by 3 so that the x's and y's can cancel out. it doesn't really matter which, but I'll go with the first one.

`9x + 3y = 99`

`x + 3y = 19`

• Subtract one equation from the other. (Tip: look for the equation with the larger coefficient for x so it ends up positive!)

`8x = 80`

• Solve for x.

`(8x)/(8) = (80)/(8)`

`x = 10`

• Plug x back in one of the equations from the original system. Either works! Now, solve for y.

`x + 3y = 19`

`10 + 3y = 19`

`3y = 19 - 10 = 9`

`(3y)/(3) = (9)/(3)`

`y = 3`