Apple and Blackcurrant: To make a 60ml concentrate the calculation would be...

[TheReverend]

Hello thanks for looking, hope I’m posting in the right forum and have worded this correctly to get the result I’m look for, so here goes...

[FONT=&quot][FONT=&quot]To make a 60ml concentrate the calculation would be...[/FONT][/FONT]
[FONT=&quot][FONT=&quot]If 10ml of 60ml was already 100% Apple and to make the mix complete the final 60ml mix including the 10ml needed to be 70% Apple and 30% Blackcurrant, how would you work out what % of Apple and Blackcurrant are needed to mix up the 50ml.

Thanks in advance [/FONT][/FONT]

 

[tkhunny]

Pick your individual beverage components and equate the VOLUME, not the percent.

Apple 10 ml * 100% + Apple (some ml) * 100% = Apple Mixture 60 ml * 70%

Alternatively

Other (some ml) * 100% = Mixture 60 ml * 30%

Just one piece at a time. I recommend doing it both ways an making sure you get the same answer, twice.

In the future, please read the forum guidelines and show YOUR best work. You just got one for free.

 

[TheReverend]

Hello @tkhunny

Thanks for that, i’ll Have a play when I get in, and see what happens as I may need to change Apple ml and percentage ratios for end result, it seems from your calculation though that this can be modified to my needs, much appreciated.

by the way I did read the rules although I couldn’t include my working out as every time I looked at the problem my brain hurt ?, so I kinda had none just a headache.

thanks again for the freebie ?

 

[TheReverend]

[FONT=&quot][FONT=&quot]So if 40ml already contains Apple...[/FONT][/FONT]
[FONT=&quot][FONT=&quot]And you need 20ml to make up 60ml of concentrate although the ratio of the end result should be 70% Apple and 30% Blackcurrant, to split the last 20% and take into account the end result already contains 40ml of Apple, then the 20ml of concentrate would have to be split...

heres my working out...[/FONT][/FONT]
[FONT=&quot][FONT=&quot][/FONT]
[/FONT]
[FONT=&quot][FONT=&quot]70% of 60 = 42[/FONT][/FONT]
[FONT=&quot][FONT=&quot]70% of 20 = 12[/FONT][/FONT]
[FONT=&quot][FONT=&quot]30% of 60 = 18[/FONT][/FONT]
[FONT=&quot][FONT=&quot]30% of 20 = 6[/FONT][/FONT]
[FONT=&quot][FONT=&quot][/FONT]
[/FONT]
[FONT=&quot][FONT=&quot]End result 42ml Apple 18ml Blackcurrant.[/FONT][/FONT]
[FONT=&quot][FONT=&quot][/FONT]
[/FONT]
[FONT=&quot][FONT=&quot]Already got 40ml Apple...[/FONT][/FONT]
[FONT=&quot][FONT=&quot]So the 20ml needs to be spilt into, 2ml Apple, 18ml of blackcurrant...

[/FONT][/FONT]
[FONT=&quot][FONT=&quot]So the 20ml mix needs to be 10% Apple as 2 is 10% of 20 &[/FONT][/FONT]
[FONT=&quot][FONT=&quot]90% of Blackcurrant as 18 is 90% of 20.

then when the 40ml Apple and the 20ml Apple and Blackcurrant are mixed the final result is exactly 70% Apple & 30% Blackcurrant[/FONT][/FONT]
[FONT=&quot][FONT=&quot][/FONT]
[/FONT]
[FONT=&quot][FONT=&quot]This works perfectly, although there must be an easier way lol.[/FONT][/FONT]

 

[stapel]

To make a 60ml concentrate the calculation would be...
If 10ml of 60ml was already 100% Apple and to make the mix complete the final 60ml mix including the 10ml needed to be 70% Apple and 30% Blackcurrant, how would you work out what % of Apple and Blackcurrant are needed to mix up the 50ml.

First, shame on the author for creating such a poorly-written exercise. It's no wonder you're confused!

Here's how a standard textbook would write what (I suspect) this exercise means:

---

You have two inputs: 100% apple juice and 100% black-currant juice. You need to make a mixture of these two juices, in which 70% of the mix is the apple juice, and 30% of the mix is the black-currant juice. You need to end up with 60 milliliters (mL) of mixed juice.

Before you got to work, somebody already got started on the mix by putting 10 mL of apple juice into the vat. You're not allowed to empty this juice from the vat, so you'll have to work with what has already been done. How much more of each of the input juices do you need to add, in order to achieve the required result?

---

Does that make better sense at all...?

heres my working out...

70% of 60 = 42
70% of 20 = 12
30% of 60 = 18
30% of 20 = 6

What is the thinking for these computations? (I'm not understanding why they're being viewed as necessary...?)

End result 42ml Apple 18ml Blackcurrant.

Already got 40ml Apple...
So the 20ml needs to be spilt into, 2ml Apple, 18ml of blackcurrant...

So the 20ml mix needs to be 10% Apple as 2 is 10% of 20 &
90% of Blackcurrant as 18 is 90% of 20.

then when the 40ml Apple and the 20ml Apple and Blackcurrant are mixed the final result is exactly 70% Apple & 30% Blackcurrant

This works perfectly, although there must be an easier way lol.

Yes, there is! Try using what you learned about percentages:

a. What is 70% of 60? (Hint: Multiply.)

b. So how many mL, in total, need to be apple juice?

c. Then how many mL, in total, need to be black-currant juice? (Hint: Subtract.)

d. How many mL of apple juice do you already have?

e. So how many more mL of apple juice do you need? (Hint: Subtract.)

f. How many mL have you added?

g. Of that amount, what percentage was apple juice? (Hint: Divide.)

h. What percentage was black-currant juice? (Hint: Divide.)

That's it!

 

[TheReverend]

Lol Hello @Denis

thanks for that yes it does make a lot more sense now, I will have a play as I’ve got loads to work out, all end results need to be 70% Apple and 30% Blackcurrant. Yet the all have varying degrees of Apple in them already, 10ml, 20ml, 30ml & 40ml.

then I need to do the same again with 60% Apple and 40% blackcurrant and 80% Apple and 20% Blackcurrant as above each with 10ml, 20ml, 30ml and 40ml of Apple already in the glass.

then work out what the ratio of each of the 10ml, 20ml, 30ml and 40ml need to be as a percentage, phew.

i’ll have a play around with your formula and see how I get on.

many thanks

 

[TheReverend]

a. What is 70% of 60? (Hint: Multiply.)

b. So how many mL, in total, need to be apple juice?

c. Then how many mL, in total, need to be black-currant juice? (Hint: Subtract.)

d. How many mL of apple juice do you already have?

e. So how many more mL of apple juice do you need? (Hint: Subtract.)

f. How many mL have you added?

g. Of that amount, what percentage was apple juice? (Hint: Divide.)

h. What percentage was black-currant juice? (Hint: Divide.)

That's it!

So... if the final result needed to be 80% Apple and 20% Blackcurrant and someone already put 30ml of apple in the vial

a. 80% of 60 = 48
b. So 48ml needs to be Apple
c. So 60 - 48 = 12ml needs to be blackcurrant
d. Already got 30ml of Apple
e. Someone put 30ml Apple in the vial so 48 - 30 = 18ml more Apple needs to be added
f. So I added 30ml in total to the vial 12ml + 18ml = 30ml
g. So I added 18ml of Apple so 18 is 60% of 30
h. Blackcurrant added was 12ml so 12 is 40% of 30

So the the 30ml needs to be 60% Apple and 40% Blackcurrant.
So when the 30ml mix is added to the Apple already in the vial the whole mix will be 80% Apple and 20% Blackcurrant?

I think ?

?

 

[JeffM]

So... if the final result needed to be 80% Apple and 20% Blackcurrant and someone already put 30ml of apple in the vial

a. 80% of 60 = 48
b. So 48ml needs to be Apple
c. So 60 - 48 = 12ml needs to be blackcurrant
d. Already got 30ml of Apple
e. Someone put 30ml Apple in the vial so 48 - 30 = 18ml more Apple needs to be added
f. So I added 30ml in total to the vial 12ml + 18ml = 30ml
g. So I added 18ml of Apple so 18 is 60% of 30
h. Blackcurrant added was 12ml so 12 is 40% of 30

So the the 30ml needs to be 60% Apple and 40% Blackcurrant.
So when the 30ml mix is added to the Apple already in the vial the whole mix will be 80% Apple and 20% Blackcurrant?

I think ?

?

Put your answer back into the original problem.

\(\displaystyle 30 + 30 = 60.\) That checks.

\(\displaystyle 0.6 \times 30 = 18.\)

\(\displaystyle 18 + 30 = 48.\)

\(\displaystyle 0.8 \times 60 = 48.\) That checks.

Learn to check your work; it is not complete until checked.

 

[TheReverend]

Ok thanks @tkhunny @staple @Denis and @JeffM

So 80% of 60 = 48 (0.8 * 60)
And 60% of 30 = 18 (0.6 * 30)

its easy to work out that bit, although I do it the long way round I just say what’s 10% of 60 = 6 then x that 6 x 8 = 48
And 10% of 30 = 3 then times that by 6 = 18

And to check my work I type in Bing 60% of 30 and it tells me

60% of 30 = 18

Not pretty but it’s the only way I can do it in my head ?

Then for working out the percentages of the Apple and Blackcurrant mix, I’m not too sure on the calculation, although it would be handy to know you guys have shown me that the answer is kind of already there.

I usually just use Bing and type 18 as a % of 30

and is says

18 is 60% of 30 ?

So now I’m wondering how Bing works out X as a percentage of Y and how would all of these calculations go into one big sum, with brackets and stuff so that if you had an imaginary calculator that had a drop down box to choose the ratio for the final concentrate at either 80/20 70/30 or 60/40 and a box to input how much Apple was in the vial already. Then a calculate button, which would show exactly what amount of Apple and Blackcurrant in ml would need to be added to the extra mix to make the total mix whichever ratio was chosen in the drop down box and also display the ratio in percent for the additional mix. That would be cool.

So in the imaginary calculator if 80/20 were chosen from the drop down field and 30ml was input into the field for how much Apple was already in the vial (using the last example), behind the scenes the imaginary calculator would go...

30 - (0.8 * 60 - 30)
Which would give (18ml Apple) and 12ml Blackcurrant
Then hopefully the calculator would have an internet connection and ask Bing
100 - (18 as a percentage of 30)
which would give 60/40

?