Question

Tue’s math teacher gave 20 four-question pop-quizzes throughout the first semester.
Tue remembered that she scored either 75% or 100% on all of the quizzes. If her
average quiz grade for the semester is 90%, how many of each score did she earn?

Answer 1

let x = the number of scores that were 75%
let y = the number of scores that were 100%

x + y = 20 and (0.75)x + (1.00)y = (20)(0.90)

Now, you have 2 simultaneous equations in 2 variables, so just solve for x and y.

Answer 2

okay.

Answer 3

If you have any difficulties at this point, just let me know.

Answer 4

x=16 y=4

Answer 5

is that close?

Answer 6

Well, "close" is hard to say. It's not correct if that's what you are asking.

Are you able to use substitution or elimination?

Answer 7

This particular problem lends itself very easily to elimination. If you rearrange the first equation, you get:

y = 20 - x

If you put that into equation #2 you get:

(0.75)x + (1.00)(20 - x) = (20)(0.90)

which gives easy numbers to work with. Now you have one equation in one variable "x". Can you solve for "x"?

Answer 8

i tried that and got the work right. But x came out as 16....again

Answer 9

x=0.8?

Answer 10

np, I'll show you what I did:

(0.75)x + (1.00)(20 - x) = (20)(0.90) -> (0.75)x + 20 - x = 18

(0.25)x = 2 -> x = 8

So, y = 12

Answer 11

wouldn't it be -.25?

Answer 12

No.

Answer 13

ok thanks for your help

Answer 14

You're welcome!