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Solutions x, y and z are mixed at a ratio of 5:7:9 [#permalink]
29 May 2006, 05:10

Solutions x, y and z are mixed at a ratio of 5:7:9 respectively in order to formulate one batch of 273 gallons of Brand X cleaning fluid. If the supplier of the solutions mixed up the order and supplied 20 gallons less of solution x, 28 gallons more of solution y and 54 gallons less of solution z, how many gallons of Brand X could be made?

Hallo raaja,
We need 273 gallons of brand X. Then brand X will contain 273/21=13 gallons of each part multiplied b y the respective ratio. Or x-65, y-91,z-117. When we take into account the confusion of the supplier, we have x 45,y-119, z-63. If we take z=9*7 then we need of each component 7 gallons or x-35,y-49, z-63 and the mixture would be 147 gallons in total

Hallo raaja, We need 273 gallons of brand X. Then brand X will contain 273/21=13 gallons of each part multiplied b y the respective ratio. Or x-65, y-91,z-117. When we take into account the confusion of the supplier, we have x 45,y-119, z-63. If we take z=9*7 then we need of each component 7 gallons or x-35,y-49, z-63 and the mixture would be 147 gallons in total

I got E too, using the same approach. However, I made a couple silly errors along the way, glossing over the line that 28 gallons MORE of solution y was supplied.

Shows I gotta be more careful when reading to avoid silly mistakes.

Re: problem on Mixture [#permalink]
31 May 2006, 09:26

raaja wrote:

Solutions x, y and z are mixed at a ratio of 5:7:9 respectively in order to formulate one batch of 273 gallons of Brand X cleaning fluid. If the supplier of the solutions mixed up the order and supplied 20 gallons less of solution x, 28 gallons more of solution y and 54 gallons less of solution z, how many gallons of Brand X could be made?

a) 231 b) 189 c) 158 d) 156 e) 147

= [{(273/21)(9) - 54}/9]21= 147

consider z cuz it is supplied by large reduction. therefore, the qty of z determines the qty of X.

if y were greately reduced, then it would be taken for the calculation.

Now, this is the point where you need to figure out, which one should be the limiting quantity. Thankfully, it's pretty easy in this case as z is the one that limits the other two.

Thus, if z=63, one part = 63/9 = 7 litres.
x= 5*7 = 35 litres, and y= 7*7 = 49 litres.