Patterns, Relationships, & Algebraic Thinking - Need Help?

The answer you want is a ratio: x miles per 8 centimeters. Ratios can be expressed as fractions, so our goal is

x miles

______

8 cm

We also have a second ratio: 3 cm per 60 miles. 3 cm per 60 miles is the same as 60 miles per 3 cm. Convert that to a fraction:

60 miles

_______

3 cm

Now, to solve.

60 miles $$ x miles

_______ = ______

3 cm $$$$ 8 cm

(Pretend the dollar signs don't exist--they're just there to get the fractions to line up.)

Solve for x miles. Multiply both sides by 8 cm to get

60 miles * 8 cm

____________ = x miles

3 cm

480 miles * cm

____________ = x miles

3 cm

160 miles * cm

____________ = x miles

cm

Anything/anything = 1 as long as the anything in question isn't zero.

2/2 = 1.

3/3 = 1.

It doesn't even have to be numbers. Units work as well.

mile(s)/mile(s) = 1

pizza(s)/pizza(s) = 1

And, the one we're interested in right now:

cm/cm = 1

We can replace cm/cm with 1/1.

180 miles * 1 = x miles.

__________

1

The answer is 180 miles.

(correction)

D.

I thinks it's called a ratio. (I'm rusty)

3 cm is to 60 miles as 8 cm is to m miles.

Solve for m

(3/60)/8 = m

(1/20)x (1/8) = m

Or, every cm is 20 miles. So, 8 cm is 160 miles

the answer is A (i do believe anyway) .

3cm=60miles

so divide 60 by 3 (60/3) to get what 1cm is equal to

then therefore it'd be 8 times that to know the equivalent of what 8cms would be.

Try this website

http://mathforum.org/dr.math/

He will explain how