Question

Grade 10 SYSTEM OF EQUATIONS QUESTION
DONT ANSWER IT, JUST HELP ME PLEASE

Fran and Winston have a combined income of 80 000 dollars. One quarter of Winston's income is the same as one-sixth of Fran's income. How much does each person earn?

Answer 1

what you need to do is create 2 equations involving the 2 things you want to know. in this case, it's winston's income and fran's income. can you do that?

Answer 2

let x be and let y be statement? so, let x be frans income and let y be winston's income

Answer 3

okay, now look at your info and see if you can come up with 2 equations involving x and y

Answer 4

x+y=80 000?

Answer 5

great and now another

Answer 6

3/12 + 2/12 = 80 000?

Answer 7

no, that's not true

Answer 8

i'm having trouble making a second one

Answer 9

\[\left\{f+w=80000,\frac{w}{4}=\frac{f}{6}\right\} \]

Answer 10

look at this statement and see what you come up with:
One quarter of Winston's income is the same as one-sixth of Fran's income.

Answer 11

i just changed the fractions so they would have the same denominator...was that wrong?

Answer 12

no, that wasn't wrong but how is 80,000 involved? you've already captured that bit of info in your first equation

Answer 13

so it would equal 0?

Answer 14

3/12 +2/12

Answer 15

no, what is equivalent in the statement?

Answer 16

3/12 of what? 2/12 of what?

Answer 17

80 000 dollars, i think

Answer 18

That will give you your second equation.

Answer 19

read the statement again please

Answer 20

@tomhue their income... I don't know.

Answer 21

Not of 80 000 dollars, but of... yes!

Answer 22

yes, their individual incomes, not the sum of them.

Answer 23

They're asking what each person earned...

Answer 24

right but what they're saying in the statement is that one quarter of winston's income is the same as on sixth of fran's income.
what represents winston's income?
what represents fran's income?

Answer 25

x(2/12) + y(3/12) ?

Answer 26

not their sum

Answer 27

x=y

Answer 28

You're not adding them. Remember, that fraction of x is the SAME as that fraction of y.

Answer 29

x/6 = y/4

Answer 30

why is the variable where the numerator is supposed to be?

Answer 31

It's the same as saying (1/6)*(x/1) = (1/4)*(y/1). You can write it as x/6=y/4 or as (1/6)x=(1/4)y, whichever you prefer.

Answer 32

like this...\[\frac{1}{4}y=\frac{1}{6}x \Rightarrow \frac{y}{4}=\frac{x}{6}\]

Answer 33

pgpilot could you give tomhue a medal because he is helping me too, i appreciate the help

Answer 34

OHHHHH!

Answer 35

i get it now.
so my two equations would be:

Answer 36

1. x+y=80 000
2. y/4=x/6

and then im going to use substitution, so,

1. x=80 000-y

so then,

2. y/4=80 000-y/6

? but then how would you solve that?

Answer 37

it may be easier to solve the other equation and substitute in the first.

Answer 38

what do you mean?

Answer 39

\[\frac{x}{6}=\frac{y}{4} \Rightarrow x = \frac{3}{2}y\]

Answer 40

Correct. Just remember that you made:
x = Fran's income
y = Winston's income

You can solve this as a proportion if you like.
\[\frac{y}{4}=\frac{80 000-y}{6}\]
You can use the cross products method. (top left * bottom right = top right * bottom left)

Answer 41

then the first becomes \[\frac{3}{2}y+y=80,000\]

Answer 42

where did the 3 over 2 come from?

Answer 43

6/4 = 3/2

Answer 44

x/6=y/4
(x/6)*6=(y/4)*6
x = 6y/4
x = (6/4)y
x = (3/2)y

Answer 45

so, @tomhue 6y+320000-4y

Answer 46

6y = 320 000 -4y

=, not + there. Now you can use algebra to solve this way, or substituting the reverse way like pgpilot326 is using.

Answer 47

6y+4y=320 000
10y= 320 000
y=32 000
so, Winston earns 32 000

Answer 48

Yup!
Now, how much does Fran earn?
Remember that x + y = 80000. You just found the value of y.

Answer 49

so then,

x+32 000=80 000
x=80 000-32 000
x= 48 0000
Fran earns 48 000

Answer 50

wow! Thanks for the help!

Answer 51

Correct. You got your answer. Winston 32000, Fran 48000. You're welcome.

Answer 52

is there any advice you can give me on these types of questions? because I have five more like this..and I struggle with them...

Answer 53

Turn the names of people/things into variables. An amount "OF" a person's income/whatever means you multiply that amount by the variable.

1/6 of Fran's income means 1/6 * x.

There will usually be one equation adding the two variables or multiples of them to make a number. The other will probably (but not definitely) have variables on both sides.

Answer 54

could we try one more? do you have time?

Answer 55

Sure.

Answer 56

thanks so much. I'll just type it

Answer 57

In one city, taxi company A charges $5 plus $0.35/km travelled. Taxi company B charges $3.50 plus $0.50/km. For what distance is the charge the same using either taxi company? In what situations would you choose company A?

Answer 58

there isn't a total distance...and how do I find out the kilometers?

Answer 59

Turn kilometer into a variable. "Of" and "per" and "/" all are indicators for multiplication when used with a number and a unit/thing/person.

Answer 60

Let "x" be km
but what would "y" be?

Answer 61

i know the money...

Answer 62

Actually, this doesn't even look like it's a system.

You know the base cost of each company, plus the per km cost.

A = base + additional*x
B = base + additional*x
You're looking for the scenario when A = B.

Answer 63

so...its not a system of equations question?

Answer 64

You could call it a system if you wanted, but it's only one-variable. It's still worth knowing how to do.

Answer 65

A= 5+.35x
B= 3.50+.50x

Answer 66

so how do I find x?

Answer 67

Remember, you want A = B. You can use substitution.

Answer 68

one second, brb

Answer 69

ok

Answer 70

5+.35x=3.50+.50x

Answer 71

Yup! Then you solve for x like you normally would.

Answer 72

5-3.50=.50x-.35x

Answer 73

1.5=.15x

Answer 74

10 x.

Answer 75

THANKS AGAIN!

Answer 76

No problem :)

Answer 77

so now i have to find the same distances

Answer 78

a= 5+.35 (10)
a= 5+3.5
a=8.5

b=3.50+.50(10)
b=3.50+ 5
b=8.5

oh wait it was 10...

Answer 79

Oh, yeah. X was the number of kilometers. It was a one-variable system. I was just using A and B to show the cost of the companies. You wanted the same cost, so A=B.

Answer 80

i'm going to check for nine to see which is cheaper.
a=5+.35(9)
a=5+3.15
a=8.15

b=3.50+.50(9)
b=3.50+4.5
b=8

so, I would choose b because its cheaper before 10 km

a=5+.35(11)
a=5+3.85
a= 8.85

b= 3.50+.50(11)
b=3.50+5.5
b=9

SO I WOULD CHOOSE A IF I NEED TO GO 10 KM OR MORE. because its cheaper after 10km.

Answer 81

Yup! If you wanted to, you could just take the slope of the equation (coefficient of the variable in these cases). The equation with the smaller slope is cheaper in the long run.

Try not to be fooled into thinking that these problems are harder than they actually are. If it's really unbearable, just save the confusing word problems for the end of the test. Go back to them.

Answer 82

Thank you so much. You have helped me alot.