Question

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

Answer 1

Answer:

C. X=10 and y=3

Step-by-step 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.

$\frac{8x}{8} = \frac{80}{8}$

$x = 10$

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

$x + 3y = 19$

$10 + 3y = 19$

$3y = 19 - 10 = 9$

$\frac{3y}{3} = \frac{9}{3}$

$y = 3$