Question

Suppose a section of the test has 50 multiple choice questions. Ron earns one point for each right answer and loses 1/4 point for each wrong answer. Ron answered 41 questions and his score was 34 3/4. How many questions did he answer correctly? how many questions did he answer incorrectly?

Answer 1

Must use equations!

Answer 2

Okay, so think of it this way. he answered 41 problems, and his score was only 34 3/4 he for each right answer he got a total of one point let's name this variable "c" and for each wrong answer he got 1/4 of a point taken away. Let's name this variable "w". Setting up an equation what could possibly be it from here?

Answer 3

1c- 1/4w= 41 ???? i dont know i need help please

Answer 4

please help @dread907

Answer 5

Okay so your equation should be set up more like this:
Points Possible = 50
Correct Answers = C
Wrong Answers = W
Points Earned equals = 34 1/4
50 - 34 1/4 equals 15 3/4 so he got 15 1/4 points taken away
15 divided by 4 equals what.

Answer 6

3.75

Answer 7

because there are 4 quarters in one. So since that equals 3.75 then + 1/4 equals 4 questions wrong

Answer 8

but i needan equation set up

Answer 9

Yes the equation was set up as we've done this.
50 - 34 1/4 = y(we never set a variable for this.)
y divided by 4 = u(nor this)
u + 1/4 = w

Answer 10

i need with the variables c and w like i did

Answer 11

like you did*

Answer 12

@zepdrix can you help me?

Answer 13

can you please help?

Answer 14

sec reading it c:

Answer 15

ok thanks!

Answer 16

C + W = 41 <- the number of CORRECT answers and WRONG answers totals 41, because he answered 41 questions.

1C - (1/4)W = 34.75 <- The number of points is given by this equation, 1 point for a correct answer, -1/4 point for a wrong answer, and his points totaled 34 and 3/4.

So we have a system of 2 equations, and 2 unknowns. shouldn't be too bad from here. I'm getting a weird number for C though, so I wanna make sure I have this set up correctly. hmm

Answer 17

Wait what happens if he doesn't answer a question, does he lose any credit for that? Oh they don't care about that :D they just want C and W. hmm

Answer 18

lol yeah it doesnt include that info

Answer 19

Oh ok now the numbers are working out nicely :) I was just putting it into my calculator wrong a second ago.

Yah these equations should work for us.

From here, we can either apply, SUBSTITUTION, or, ELIMINATION.
Which are you more comfortable with? :D

Answer 20

substitution

Answer 21

Messing with the first equation gives us W = 41 - C.

Plugging this into the second equation gives us,\[\large C-\frac{1}{4}(W)=37.75 \qquad \rightarrow \qquad C-\frac{1}{4}(41-C)=37.75\]

Answer 22

From here you should be able to find C without too much trouble ^^ Don't forget to DISTRIBUTE the -1/4 to each term inside the brackets.

If you're still confused, you can let me know! c:

Answer 23

ok thanks alot i will do it now. after this can you help me with 2 others? :( sorry for the trouble

Answer 24

wait! isnt it 34.75?

Answer 25

you put 37.75

Answer 26

It is 34.75, yes! sorry about that c: typo

Answer 27

Yah I'll try to answer them if I'm not too busy :D Throw an @zepdrix in if I'm being too lazy XD lol

Answer 28

ok please please help me when i done with this one please please? i really need help :c

Answer 29

c=36 w=5

Answer 30

@zepdrix is that right??

Answer 31

Hmmmm I came up with different numbers XD lemme check again.

Answer 32

ok

Answer 33

\[\huge C-\frac{1}{4}(41-C)=34.75\]\[\huge C-\frac{41}{4}+\frac{1}{4}C=34.75\]\[\huge \frac{5}{4}C=45\]

\[\huge C=36\]
Yesss good job! I must've done it with the 37.75 the first time I tried it ^^

Answer 34

lol ok thanks :) can i type the 2nd +3rd questions here please?

Answer 35

@zepdrix

Answer 36

mmmmmmm fine :3

Answer 37

Sandi wants to use up 14 eggs and 12 cups of milk. How many quiches and bread pudding recipes can she make?
RECIPE:
Bread pudding: 5 cups milk and 3 eggs
Quiche: 1 cup milk and 4 eggs

Answer 38

@zepdrix

Answer 39

Hmmm this one I'm not so sure :( I'm having trouble setting up the equations. Hmmmm

Answer 40

it gives a hint, (Write a system of equations that involves the number of quiches,x and the nimber of bread pudding y and the ingredients

Answer 41

Hmm ok let's try something...

Answer 42

Bah I dunno :c soz, i suck at word problems lol

Answer 43

lol aw man :c ok ill just try my best
what about this one?
Ron has 30 nickels and dimes totaling 2.40. How many of each does he have?

Answer 44

The total number of nickles and dimes adds up to 30 coins:
\[\huge N+D=30\]
The VALUE of those coins, 10 cents per dime, 5 cents per nickle, totals 2.40:\[\huge .05N+.10D=2.40\]
So this our system.

Answer 45

Similarly to the first problem, we should be able to use SUBSTITUTION quite effectively c:

Answer 46

i set up those equations but i got weird answers :C

Answer 47

i got n= 1.2 and y=28.8

Answer 48

For the second equation, let's multiply both sides by 20 to get rid of those ugly decimals!\[\huge N+2D=48\]That might make it easier to work through :)

Answer 49

wait can we use substitution ? :c

Answer 50

Yes, Substitution is good, but it's just a good idea to get rid of the decimals before substituting c:
It's not entirely necessary though.
Substitute away! c:

Answer 51

i did and i got those answers :C idk what i did wrong

Answer 52

From the first equation we get,\[\huge N=30-D\]
Plugging this into the second equation gives us,\[\huge (30-D)+2D=48\]

\[\huge 30+D=48\]
\[\huge D=48-30\]Understand what we did there? :D

Answer 53

but wait how did you get those numbers? :o

Answer 54

2d and 48?

Answer 55

\[\huge .05N+.10D=2.40\]Multiplying both sides by 20 gives us,\[\huge 20(.05N+.10D)=(2.40)20\]
\[\huge N+2D=48\]We did this to simplify the second equation, getting rid of the decimals so it's easier to work with.

Answer 56

Confused? <:o

Answer 57

i tthink i got it 12 nickels anmd 18 dimes?

Answer 58

Yay good job \c:/

Answer 59

yay thanks :D and are you sure you dont know how to solve the egg and milk problem?

Answer 60

cause im so lost on that one :C