Question

Brad can make 4 key chains in an hour. Velma can make only 3 key chains in an hour, but she already has 6 completed key chains. Explain to Brad how he can use a system of equations to determine when he will have the same number of key chains as Velma. Please explain each step too?

Answer 1

Let t represent the amount of hours.

Answer 2

Say molly can make 3 keys per hour
than the number of keys per hour she can make is given by the expression 3t


so can you make an expression for Brad?

Answer 3

so it's the number of key chains multiplied by the amount of hours?

Answer 4

no.
M(t)=3t
because Molly can make 3 keys per hour
for example when t=1 hour then M=3 this means she has made 3 keys in 1 hour
if t=2 then M=3+3=6 this mean she has made 6 keys in 2 hours because she can make 3 keys in 1 hour

Answer 5

Say Velma has already made 2 keys and can make 5 keys an hour.
So her function would be V(t)=2+5t
because at 0 hours V=2 which this means before she began she had 2 completed keys
at t=1 she would have V=7 this means she has had 7 completed keys after 1 hour

Answer 6

You can find when they have the same number of keys by setting M(t)=V(t)
by solving the following for t:
3t=2+5t

Answer 7

So try making an expression for Brad and Velma.

Answer 8

okay, one second while i do that.

Answer 9

Oops didn't realize you had a velma
someone said something about velma so i thought she wasn't being used

Answer 10

my velma is different from your velma

Answer 11

Brad can make 4 key chains in an hour.
This means in 1 hour he can make 4.
In 2 hours he can make 4+4=2(4)=8.
In 3 hours he can make 4+4+4=3(4)=12.
So in t hours he can make t*4 or 4t is how it is normally written.
B(t)=4t.
Do you see how I came up with that?

Answer 12

do i have it right so far?

Let (t) represent the amount of hours. Let (V) represent Velma and (B) for Brad.

Since Velma is able to make 3 key chains per hour, vt = 3t.

Brad will be able find when he will have the same number of key chains by setting B(t)=V(t)

Solve for (t).
4t = 6 + 3t

Answer 13

you did it !: )

Answer 14

B(t)=4t
and
V(t)=6+3t

Answer 15

4t=3t+6

try subtract 3t on both sides

Answer 16

Solve for (t).
4t = 6 + 3t

Subtract 3t on both sides.
4t - 3t = 6 + 3t - 3t

Dive 1t by both sides.
1t = 6

t=6

Answer 17

is that correct?

Answer 18

yeah! :)
so in 6 hours they will have same amount of key chains made

Answer 19

np
sorry for using you velma in my example

Answer 20

:p

Answer 21

no worries