Problem Solving

How much tea worth 0.93$ per pound
must be mixed with tea worth $0.75
per pound to produce 10 pounds worth
$0.85 per pound?

1) 2 2/9
2) 3 1/2
3) 4 4/9
4) 5 5/9
5) 9 1/2

OA is D

grandh01 wrote:How much tea worth 0.93$ per pound
must be mixed with tea worth $0.75
per pound to produce 10 pounds worth
$0.85 per pound?

1) 2 2/9
2) 3 1/2
3) 4 4/9
4) 5 5/9
5) 9 1/2

OA is D

Set up and equation for the unknown variable x. x=the amount of $.93 we want
so...
.93x+.75(10-x)=10*.85
.93x+7.7-.75x=8.5
.18x=1.0
x=1.0/.18 = 10/1.8 (or about 10/2 = 5) our answer will be 5 something. Only answer with a 5 is D... Go with D.

You asked a similar question in a previous post. Do you understand how I set up the equation .93x+.75(10-x)=10*.85?

On the GMAT it is imperative to set up your equations correctly and with only one variable. For example, previously I used to set up the equation as .93x+.75y+8.5. This will NOT work because we have two variables and only one equation!

So.. how should we set up a "smart" equation? Always set x (or whatever) equal to whatever you are looking for (this saves time). In the problem set x = to the amount (in pounds) of the .93 tea. Now to create the equation: We know that there are going to be 10 pounds on tea. If we have x pounds of .93 tea, will will have 10-x pounds of the .75 tea.
Now we know:
x = .93 tea (A tea)
10-x = .75 tea. (B tea)
We also know that both teas will equal ten pounds of .85 per pound (C tea). So lets set it up:
A + B = Ten pounds of C, or
.93x + .75(10-x) = .85*10.
Now solve like I did above.
Hope this helps!

grandh01 wrote:How much tea worth 0.93$ per pound
must be mixed with tea worth $0.75
per pound to produce 10 pounds worth
$0.85 per pound?

1) 2 2/9
2) 3 1/2
3) 4 4/9
4) 5 5/9
5) 9 1/2

OA is D

If you're not comfortable with decimals, you can see that if we multiply every amount by 100, it's not going to make any difference. So, question can be rephrased (or understood):

How much tea worth 93$ per pound must be mixed with tea worth $75 per pound to produce 10 pounds worth $85 per pound?

Now setup the equation: 93(x) + 75 (10 -x) = 10 * 85
=> 93x + 750 - 75x = 850
=> 18x = 100
=> x= 100/18 = 50/9
Choose D.

grandh01 wrote:How much tea worth 0.93$ per pound
must be mixed with tea worth $0.75
per pound to produce 10 pounds worth
$0.85 per pound?

1) 2 2/9
2) 3 1/2
3) 4 4/9
4) 5 5/9
5) 9 1/2

OA is D

Well one of the short cut approach could be like this.

There are 2 kinds of Tea- $0.93/pound, & $0.75/pound to make $0.85/pound. Whenever 2 quantities are mixed to produce another mixture, weighted average concept comes into picture.

Approach 1

Since final mixture is $0.08 distant from Ist tea, & $0.10 distant from IInd Tea, hence more of Ist tea than IInd tea should be mixed(0.08<0.10). Total quantity mixed is 10 pound of 2 tea. There are 2 options that may be answer- Options D), & E). The closest rational answer should be D). We disqualify E, because 9 1/2 is almost all of Ist tea, only 1/2 pound of IInd tea.

Approach 2

When 2 quantities having weights as a, & b are mixed to get a mixture of x weight, then mixing ratio comes out to be [|b-x|/|x-a|].

With reference to this question, we can say that 2 tea should be mixed in the ratio of 0.10:0.08 = 10:8=5:4.

So the quantity of Ist tea out of 10 pounds would be 5/4*10=5 5/9 pound.

grandh01 wrote:How much tea worth 0.93$ per pound
must be mixed with tea worth $0.75
per pound to produce 10 pounds worth
$0.85 per pound?

1) 2 2/9
2) 3 1/2
3) 4 4/9
4) 5 5/9
5) 9 1/2

OA is D

The price of the mixture -- 85 -- is a little closer to 93 than to 75.
Thus, a bit more than 1/2 of the 10 pounds must be composed of the 93-cent tea.

The correct answer is D.

ALWAYS LOOK AT THE ANSWER CHOICES.

(0.93(x) + 0.75(10 - x))/(10) = 0.85

0.18(x) + 7.5 = 8.5

x = 100/18 = 50/9 = 5 5/9

Choose option 4.