Need help with mathematical question? The answer is 40? how do you get to that point?

Question

A certain preparation consists of liquids x, y, and z in the proportion 5:2:1. How many gallons of the preparation can be made from a stock of materials consisting of 25 gallons of x, 20 gallons of y, and 8 gallons of z?

Can anyone please show me how you reach to the answer? Any help will be much appreciated and thanks a lot!! :)

Answer 1

The first thing you need to do is figure out which of the three liquids is going to be the one that limits the maximum quantity of the mixture that can be made. Since the ratios are 5:2:1 you need 5 parts x, 2 parts y, and 1 part z. You have 25 gallons of x and, if that's 5 'parts' then 1 'part' must be 5 gallons. Now you need 2 'parts' (or 10 gallons) of y, and you do have that much in stock. Lastly 1 'part' (5 gallons) of z is required and you have that much in stock as well. So you'll mix 25 gallons (5 'parts') of x, 10 gallons (2 'parts') of y, and 5 gallons (1 'part') of z for a total of 25+10+5 = 40 gallons of the mixture.

Hope that helps.


Doug

Answer 2

the 1 in 5:2:1 can only be the liquid z of 8 gallons
with z as 5 gallons
x=25 gallons (5 times z)and y 10 gallons (2 times z)
so you can prepare 40 gallons with 25 gallons of x,10 gallonsof y and 5 gallons of z

Answer 3

One of the liquids is the limiting factor.

It's like scaling up a recipe.

Using liquid x, you could scale up by a factor of 5.
With liquid y, you could scale up by a factor of 10.
With liquid z, you could scale up by a factor of 8.

Liquid x is the limiting liquid. You have only enough of x to scale the whole recipe up by a factor of 5.

You can use 25 gallons of x, 10 gallons of y, and 5 gallons of z. That adds to 40 gallons in the correct proportion.

Answer 4

Proportion must be :
5 gallons of x : 2 gallons of y : 1 gallon of z

Now add another equal amount of each. This gives :
10 gals of x : 4 gals of y : 2 gallons of z

Add another lot to give :
15 gals of x : 6 gals of y : 3 gals of z

And another to give :
20 gals of x : 8 gals of y : 4 gals of z

One more time :
25 gals of x : 10 gals of y : 5 gals of z

We have now used up all the stock of x.

The number of gallons of preparation is
now equal to 25 + 10 + 5 = 40 gallons.

Answer 5

its very simple like
no of total liquid gallons must equal to 40
now percentages are given which are

5:2:1

now

5+2+1=8
it means proportion of X is 5 out of 8

and the value of X

5/8*40=25

and

Value of Y

2/8*40=10

and

Value of Z

1/8*40=5

So Proportion of

X : Y : Z

25 : 10 : 5

Answer 6

permit the pounds required of the $8 tea be y.considering he has to create a 60 pound combination,the pounds of $6 tea would be (60-y) .So 8y+6(60-y)=7.4*60.The Left hand component of this equation is the complete weight of the tea that he bought,that's the burden of $8 pound tea + weight of $6 pound tea.precise hand component denotes the burden of the tea he bought for $7.40,considering those are an identical 2 parts,they could be equivalent.remedy to get y=40 two pounds.So he will require 40 two pounds of the $8 tea and (60-40 two)=18 pounds of $6 tea.;)