RATIOS QUESTION - BRAIN FREEZE!!!!!

[cyruscyrus]

Can someone help me work this problem out? I am so burnt out and my brain freeze is not allowing me to get over this hurdle:

A sporting goods stores ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratios of the white balls to yellow balls 6:5. Hw many tennis balls did the store originally order?

A. 120
B. 150
C. 180
D. 300
E. 330

If possible, show me how you worked it out. Because I already know the right answer is D.

[kath_the_great4]

let x be number of balls ordered of either color.

6/5= x+30/x
6x=5x + 150
x= 150

total order is 2x = 300 (since equal number of both colors ordered)

[cyruscyrus]

Can you tell me why you have the /x on the right hand of the equation??


I get why its 6/5 = x+30 but why x+30/x???

[elmiko]

If it helps, here's how i thought of it.

They intended to order an equal amount of each color, a 1:1 ratio. a 5:5 ratio = 1:1.

Since 30 extra balls made the ratio 6:5, then 30 equals 1/5th of the intended order for each color. So 5*30 + 5*30 = 300.

[sumidi]

Adding onto elmiko,

I actually did this question without picking up the pen.

This is what I did, the question is saying that that the ratio of the balls was 6:5.

I instantly realized that 6/11 of X number must be equal to white balls.

Now we know the balls cant be 1/2 or 3/4 of a ball. So I quickly scanned the list and there was only choice which multiplied with 6/11 cleanly. 330. Now i remembered we added 30 so I subtracted that and I got 300. Sometimes its good when the examiners try to trick us with tempting answers.

Did I over-simplify this?

Sumi

[jbramet]

I think the most academic and simple way (without shortcuts of any sorts) is

W/Y = 1/1
&
(W+30)/Y=6/5

Simplification of first ratio gives: W = Y

Simplification of 2nd: 5(W+30) = 6Y therefore 5W + 150 = 6Y

Finally, as Y=X we have 5W + 150 = 6W

W= 150 therefore Y = 150 therefore total of W + Y = 300

I do not know but it seems clearer to me to think about it as a system of equation...

JB

[cramya]

Let x be the white
Let y be the yellow

x/y = 1/1 i.e x=y

When u add 30

x+30/y = 6/5
5x+150 = 6y

5y+150 = 6y ( x=y)

y=150 x=150 D)