Question

Help on a long Question?

Answer 1

Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math. To help her concentrate better on math, she spends 20 minutes more dancing than doing math.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she practices dances every day (y). (5 points)

Part B: How much time does Pam spend on practicing math every day? (3 points)

Part C: Is it possible for Pam to have spent 60 minutes practicing dance every day? Explain your reasoning. (2 points)

Answer 2

So she spends 30 minutes practicing math every day and 50 practicing dance

Answer 3

Part C is no i can do that

Answer 4

i just need help with part A

Answer 5

How many minutes per day does she study math? the answer is just a letter. can you answer?

Answer 6

she studies 30 minutes per day of math

Answer 7

just a letter?

Answer 8

yes, just a letter. Read
he relationship between the number of minutes Pam practices math every day (x)

Answer 9

oh ok so its x

Answer 10

and how many minutes dancing ?

Answer 11

y

Answer 12

so the equations wouls be 80=x+y and y=x+20?

Answer 13

yes

Answer 14

Oh ok Thank You!

Answer 15

if you solve them, you will find x= 30 and y = 50

Answer 16

oh ok like i put all the way up?

Answer 17

wait would it be x=80-y?

Answer 18

yes.

But it would be good to show the work (or least know how to do it )

Answer 19

i did it menatlly lol but ok i see your point Thanks :)

Answer 20

two ways:
elimination. write both equations so the variables are all on the same side, in alphabetical order.
80=x+y and y=x+20 become
x+y= 80
-x + y= 20
add the two equations
(x-x) + 2y = 100
0 + 2y = 100
2y= 100
y = 50

then use y=50 in x+y= 80 to find x+50= 80 and x= 80-50= 30

Answer 21

substitution
we have
x+y= 80
y=x+20

replace y in the first equation with the equivalent x+20 to get

x+ x+ 20= 80
simplify to get 2x+20=80
2x= 80 - 20
2x= 60
x= 30 (divided both sides by 2)

and find y= x+20 using x=30
y = 30+20
y= 50


substitution works well for only 2 variables. For more than 2, elimination is easier (if you know matrices)

Answer 22

I haven't seen matrices in my text book yet lol. And Thanks For all your help i really appreciate it.

Answer 23

yw.

No, solving 3 equations with 3 unknowns is a pain.

But I would learn how to solve the 2 equations using algebra. Figuring out the answer in your head is *harder* than learning the algebra way. And algebra will work for harder problems.

Answer 24

** I meant matrix ideas show up for 3 equations (or more), and typically not seen for 2 equation problems

Answer 25

All i did was subtract 20 from 80 and divide by 2 then add that 20 to one of the 30s' in the pair it was relatively easy

Answer 26

Then figured x+y=80 because dance + math = 80 mins and math + 20=dance

Answer 27

yes. and the "algebra way" is just writing down the equation so it is clear what the steps are.

A lot of people would be clueless that they should
"subtract 20 from 80 and divide by 2 then add that 20 to one of the 30s' in the pair"

How do you explain that that is the right thing to do? Algebra is one way...

Answer 28

lol i guess but thanks (again) lol