Question

Solve and explain using a chart and algebra

Answer 1

Jack plants two varieties of Bean stalks. Variety A was 12 inches tall when planted and grow 6 inches per day. Variety B was planted the same day, was 30 inches tall and grows 3 inches each day. When will the bean stalks be the same height?

Answer 2

Please help me explain this and solve it by using a chart and algebra (no need for graph)

Answer 3

let's use x to represent number of days

"Variety A was 12 inches tall when planted and grow 6 inches per day."

growth rate can be expressed as 6 * x, then add on the 12 inches the plant already had to begin with, to get

height of A = 6x + 12

repeat this process with plant B

then set the equations equal to each other to get the time when the beanstalks are the same height

Answer 4

They both have the same height is the 6th day with the same height of 48 inches but im not sure how to put this onto a table

Answer 5

Y = 6x + 12
Y = 3x + 30

Answer 6

@Vocaloid

Answer 7

oh, a table

you just need to make two columns, 1 for the day and 1 for the height

Answer 8

*three columns, sorry

Answer 9

then to fill out the first row, you'd calculate the heights of the plants on day 1, fill them into the table, then keep going until both A and B have the same height, then you can stop

Answer 10

do i do a table for each variety?

Answer 11

you can combine them into 1 table

so the first column is days, second column is height of plant A, third column is height of plant B

Answer 12

ohh

Answer 13

for some reason they both dont meet on day 6... did i do something wrong

Answer 14

@Vocaloid

Answer 15

two things, the table should technically start at 0 since on day 0 the plants were planted,

your calculations are correct, you need to keep going, the heights should be equal at 48 not 42

Answer 16

OH

Answer 17

yeah, in order to get the right value the heights need to be the same on the same day (same row)

Answer 18

so for day 1, id put both to heigh 0?

Answer 19

"Variety A was 12 inches tall when planted and grow 6 inches per day. Variety B was planted the same day, was 30 inches tall and grows 3 inches each day"

so the height on day 0 (planting day) is 12 for A and 30 for B

Answer 20

it still doesnt look right

Answer 21

Thank u... that makes much more sense.... Ive done the graph part and then we did the table part and now i have to do the algebra part.... how do u think i could start this?

Answer 22

algebraically?

you have two equations

Y = 6x + 12
Y = 3x + 30

we can set them equal to each other and solve for x

6x + 12 = 3x + 30

know where to go from here?

Answer 23

can u show me what to do next... im rly bad at math lol i get rly confused

Answer 24

cuz i ended up with this @Vocaloid

Answer 25

hm not quite you should have ended up with x = 6 as per our table

Answer 26

6x + 12 = 3x + 30

try subtracting 3x from both sides

Answer 27

wouldnt u divide 3 from both sides

Answer 28

sure, you can do that if you'd like

Answer 29

hows this

Answer 30

the x's don't just disappear
also you have to apply the /3 to every term

Answer 31

( 6x + 12 ) / 3 = 2x + 4
( 3x + 30) / 3 = x + 10

Answer 32

ohhh

Answer 33

there we go

Answer 34

good
then you'd subtract x from both sides

Answer 35

uhh does subtracting x do anything

Answer 36

at this point you have

2x + 4 = x + 10

subtracting x from both sides will eliminate x from the right side, thus making it so that x is only on one side

Answer 37

oh ok

Answer 38

2x - x is x, not 2x

so at this point you should have x + 4 = 10

then you just need to subtract 4 from both sides, that should end up w/ x = 6

Answer 39

thanks.... a lot.... B)

Answer 40

What about the height? (48), where would i put this into an algebraic equation?

Answer 41

solving for x gave us the number of days to reach equal height

so plugging x into either

Y = 6x + 12
or
Y = 3x + 30
should give 48 as the result both ways

Answer 42

oh ok B)