Question

A local pet groomer must clip the nails of 40 birds and cats. If there are 110 feet, how many birds are there? How many cats?

Answer 1

There are 2 unknowns. # of birds and # of cats

First step: give these unknowns a "name" : a single letter variable.
Can you do that ?

Answer 2

B=birds C=cats

Answer 3

ok. But be clear... B is the NUMBER of birds. same for C
now when the question says
"40 birds and cats"

what does that mean ? B+ C = ?

Answer 4

A total of both. So I could use X.

Answer 5

We don't want any more unknowns.
Think like this:
The number of birds plus the number of cats is what ?

Answer 6

you want to match that with the idea of "40 birds and cats"

Answer 7

I don't understand

Answer 8

A local pet groomer must clip the nails of 40 birds and cats.

How many birds and cats will be groomed ?

Answer 9

40

Answer 10

and if you groom B birds and C cats, you groom B+C animals
or B+C birds and cats
what is B+C equal to ?

Answer 11

40

Answer 12

yes. we write that as
B+C= 40

that is one equation. Because we have 2 unknowns, we will need 2 equations if we want to solve the problem.

Answer 13

They tell us
there are 110 feet

How many feet do C cats have ?

Answer 14

4

Answer 15

1 cat has 4 feet.
2 cats have 2*4 feet
3 cats have 3*4 feet
C cats have ?

Answer 16

x feet

Answer 17

follow the pattern
1 cat has 4 feet.
2 cats have 2*4 feet
3 cats have 3*4 feet
4 cats have 4*4 feet
5 cats have 5*4 feet
C cats have ?

(remember C means "number of cats". It will be a number... we don't know what the number is, but it is a number)

Answer 18

Okay

Answer 19

if C were 3, how many feet would you have ?

Answer 20

12

Answer 21

how did you get 12 ?

Answer 22

12 is correct. But how did you figure it out ?

Answer 23

you probably multiplied 3 times 4 (3 cats times 4 feet per cat is 12 feet)
if you have C cats, you do the same thing. you multiply C times 4
in algebra, to show a letter times a number we write
4*C or just
4C

4C is the number of feet C cats will have

Answer 24

ok

Answer 25

How many feet do B birds have ?
use the same idea.

Answer 26

You do know that 1 bird has 2 feet ?

Answer 27

yes

Answer 28

and you know you should multiply the number of birds by 2 to get the number of feet ?

Answer 29

yes

Answer 30

can you write down the number of birds times 2 ?

Answer 31

bc

Answer 32

BC means B times C
(which means number of birds times number of cats)

You want "number of birds" times 2

Answer 33

Okay...

Answer 34

can you write down the number of birds times 2 ?

Answer 35

b*2

Answer 36

yes, or just 2b (in algebra, we leave out the multiply sign, because people are lazy)

so, to remind ourselves,
4C is the number of feet from the cats
2B is the number of feet from the birds

the question says
there are 110 feet

Answer 37

if you add up the number of cat feet and the number of bird feet, you get 110

can you write down the equation, showing this ?

Answer 38

sorry I'm confused

Answer 39

number of cat feet plus number of bird feet is 110

use the 4C = number of cat feet
and 2B = number of bird feet
replace the words with the algebra