Question

The weight of 10,000 identical samples of a substance is 1 pound.
What is the weight of 1000 samples?

Answer 1

can you write down the ratio ?

Answer 2

i dont know how to

Answer 3

weight of 10,000 identical samples of a substance is 1 pound.

write that as
\[ \frac{ 10,000 \text{ samples} }{1 \text{ pound } }\]

Answer 4

okay

Answer 5

that ratio says 10,000 samples is "the same" as 1 pound

the question asks for weight of 1000 samples
\[ \frac{ 10,000 \text{ samples} }{1 \text{ pound } } = \frac{1000 \text{ samples} }{x \text{ pound } } \]

Answer 6

that says 10,000 samples is to 1 pound as 1000 samples is to x (unknown) pounds

to solve, "cross multiply"
can you do that ?

Answer 7

yes

Answer 8

1,000=x=10,000 ri ght ?

Answer 9

there is only one = sign when you cross multiply
try again.

Answer 10

1,000=x10,000

Answer 11

yes that is good.

Answer 12

now we use the *very useful idea*
anything divided by itself is 1
in other words divide both sides by 10,000
\[ \frac{1000}{10000} = \frac{x 10000}{10000} \\
\frac{1000}{10000} = \frac{x\cancel{ 10000}}{\cancel{10000}}
\]
we have
\[ x = \frac{1000}{10000} \]
can you simplify that ?