Question

My daughter is in Algebra 2 for home schooling, and I am her learning coach. She has a word problem that is this: A playing field: P= 450, L= 3 yds less than triple the W. What are the dimensions of the playing field. Question is How do I explain to her how to set this up. It has been 5 years since I have done this, and I am brain dead.

Answer 1

unpack
"L= 3 yds less than triple the W"

Answer 2

Length = 3 yards less than triple the Width

Answer 3

"triple with width W" would be written as \(3\times W\) or \(3W\)

Answer 4

3 yards less than triple the width: \(3W-3\)

Answer 5

so far so good?

Answer 6

for example, if the width was say \(100\) (which it is not, just an example) then the length would be 3 less than triple 100 or \(300-3=297\)

Answer 7

still lost

Answer 8

on how to figure out the Length

Answer 9

ok lets try this:
we are forgetting everything but the line "L= 3 yds less than triple the W"

Answer 10

only focusing on that one
suppose i say the width is 50
what is the length?

Answer 11

if it is not clear, let me know and we can walk through it

Answer 12

L = 147??

Answer 13

exactly

Answer 14

and suppose the width is 25
what is the length?

Answer 15

L = 72

Answer 16

k good
now we know what we are doing
how did you get your answers?

Answer 17

oopss forgetting ft

Answer 18

i don't see the mention of feet in the problem
so lets assume the units are yards, and ignore feet

Answer 19

3(25) - 3 = 3*25 = 75 - 3 = 72

Answer 20

k good
so if you know the width, you know the length
how do you find it? multiply by 3, then subtract 3
if we replace \(25\) by the variable \(W\) then the equation tells you
\[L=3W-3\] which is what "L= 3 yds less than triple the W" says in math

Answer 21

right

Answer 22

ok so that part is done
now how about this part
" P= 450"

Answer 23

kk

Answer 24

we need an expression for the perimeter in terms of the width \(W\) and length \(L\)

do you know it? ("no" is a fine answer, just asking)

Answer 25

actually . no

Answer 26

wouldn't it be p =l * w

Answer 27

so since we have the Perimeter wouldn't we divide the L and W

Answer 28

to get the Dimensions

Answer 29

that is an expression for the Area and as you see by your multiplication it comes in square units (2 dimension) if the width is 4 and the length is 3 yards, the area is \(3\times 4=12\) square yards
perimeter is a length, one dimension, a number of yards in this case

Answer 30

oooppps wouldn't we divide to get them?

Answer 31

so no, it is not \(P=LW\) but rather \(A=LW\) we need an expression for the perimeter

Answer 32

oh ok

Answer 33

measure of the perimeter is the total length
in this case it would be \(10+10+15+15=50\) or i could write (suggestively)
\[2\times 10+2\times 15=50\]

Answer 34

now with this picture
what is the perimeter?