# Thread: numerical skills and prealgebra help:)

1. ## numerical skills and prealgebra help:)

I have to take a placement test for math for school. The problem is that I haven't done any math in 2 years so my mind is a little rusty. These simple questions are stumping me.

How do you solve a problem that asks you:

1) what value of x solves the following proportion?
9/6=x/8

I thought the answer would be 11, but it apparently is 12. How do you go about getting the proper answer?

And also,
A total of 50 juniors and seniors were given a mathematics test. the 35 juniors attained an average score of 80 while the 15 seniors attained an average/ of 70. what was the average score for all 50 students who took the test?

I am so lost at how to figure this out.

any help will be greatly appreciated!

2. Originally Posted by t.d.
I have to take a placement test for math for school. The problem is that I haven't done any math in 2 years so my mind is a little rusty. These simple questions are stumping me.

How do you solve a problem that asks you:

1) what value of x solves the following proportion?
9/6=x/8

I thought the answer would be 11, but it apparently is 12. How do you go about getting the proper answer?

And also,
A total of 50 juniors and seniors were given a mathematics test. the 35 juniors attained an average score of 80 while the 15 seniors attained an average/ of 70. what was the average score for all 50 students who took the test?

I am so lost at how to figure this out.

any help will be greatly appreciated!
9/6 = x/8

There is shotcut which is cross multiplication:
(numerator1 * denominator2) = (numerator2 *denominator1), meaning,
9*8 = x*6
x = 72/6 = 12 -----answer.

Another way is to clear the fractions. Multiply all fractions by the product of all the denominators:
(9/6)(6*8) = (x/8)(6*8)
9*8 = 6*x ----------------same as above.

- - - - - - - -

A total of 50 juniors and seniors were given a mathematics test. the 35 juniors attained an average score of 80 while the 15 seniors attained an average/ of 70. what was the average score for all 50 students who took the test?

Average score for the 50 people here means total score of the 50 people divided by the total number of people---which is 50.

...the 35 juniors attained an average score of 80...
That means each of those 35 juniors got 80....supposedly.

So, for the 50 people,
Average score = (35*80 +15*70) / 50 = 77 -----answer.

3. Find $x$: $\frac{9}{6} = \frac{x}{8}$
The left fraction can be simplified as $\;\;\frac{3}{2}$

So now you have: $\;\;\frac{3}{2} = \frac{x}{8}$

Cross multiply.

In other words, if you have: $\frac{a}{b} = \frac{c}{d}$

Then you do: $bc = ad$

So you'll have: $2x = 24 \Rightarrow x = 12$

4. thanks for the help! I'm slowly starting to get the hang of this again

5. Originally Posted by Jonboy
The left fraction can be simplified as $\;\;\frac{3}{2}$

So now you have: $\;\;\frac{3}{2} = \frac{x}{8}$

Cross multiply.

In other words, if you have: $\frac{a}{b} = \frac{c}{d}$

Then you do: $bc = ad$

So you'll have: $2x = 24 \Rightarrow x = 12$
note to the OP. with simple fractions like these, where the variable is just in one location, we can save ourselves at least one step, by doing the opposite operation to what is modifying the variable. example, in this case, we could just multiply both sides by 8, why? because 8 is dividing x

$\frac 32 = \frac x8$

$\Rightarrow 8 \cdot \frac 32 = x$

$\Rightarrow 12 = x$

be careful when the variable is in the denominator. you can just flip both sides first