Question

2) Karl said, “If I divide my dog’s age by 4 and subtract 2, I get the same result as when I divide my dog’s age by 8.”
a. Write an equation you can solve to find the dog’s age.
b. Solve your equation by doing the same thing to both sides. Check your solution.

Can somebody please help me? I'm stuck after i did it over and over and got different answers.

Answer 1

the first step is give a name for the unknown (dog's age in this case). People like to use x because x stands for unknown (why?).

divide my dog’s age by 4

replace "my dog's age" with x

divide x by 4

can you rewrite that using a divide sign instead of words?

Answer 2

\[x \div 4 - 2 = x \div 8\]
How do I solve that?

Answer 3

yes that looks good. but most often people use the form
\[ \frac{x}{4} -2 = \frac{x}{8} \]
it means the same thing

one way to solve is to "get rid" of the denominators, because fractions are a pain.
multiply both sides of the equation by 8:
\[ 8 \cdot \left(\frac{x}{4} -2 \right) = 8 \cdot \frac{x}{8} \]
can you do the multiplication?

Answer 4

(x/4)-2=x/8

x/4=x/8 + 2/1

x/8 +2/1(find the lcm of 1 and 8 which is 8, then add the two fractions)

you get this x+16/8

then you bring in the x/4

x/4=x+16/8 bring four over to the right to muliply x+16

x=4(x+16)/8 four will be eliminated by eight, leaving (x+16)/2

x=(x+16)/2 take two over to the other side to multiply x

2x=x+16 take x to the left, it becomes -x

2x-x=16

x=16( dogs age)

Check: 16/4=4, 4-2=2
16/8=2

get it now?

Answer 5

Thank you phi and DrAmaQueen. You are both very helpful. I understand now.