# GCSE Higher maths ratio question

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#1
I have read the mark scheme but I do not understand why the steps are done!
would appreciate a step by step guide for this question thanks!

Ben fills a glass with orange juice and lemonade in the ratio 1 : 4 by volume. He mixes the liquid that is in the glass.
Ben drinks 1/4 of this liquid. He then fills the glass using orange juice. Work out the ratio of orange juice to lemonade, by volume, that is now in the glass. Give your ratio in its simplest form.
0
2 years ago
#2
(Original post by NelsaH)
I have read the mark scheme but I do not understand why the steps are done!
would appreciate a step by step guide for this question thanks!

Ben fills a glass with orange juice and lemonade in the ratio 1 : 4 by volume. He mixes the liquid that is in the glass.
Ben drinks 1/4 of this liquid. He then fills the glass using orange juice. Work out the ratio of orange juice to lemonade, by volume, that is now in the glass. Give your ratio in its simplest form.
Sorry we do not do questions for people - you need to have a go and then we'll give a hint.
0
#3
I have had a go and I got completely the wrong answer and basically guessed how to do it...
(Original post by Muttley79)
Sorry we do not do questions for people - you need to have a go and then we'll give a hint.
0
2 years ago
#4
(Original post by NelsaH)
I have had a go and I got completely the wrong answer and basically guessed how to do it...
So what did you try?
0
2 years ago
#5
Let use turn the ratio 1:4 to 4:16 for ease and to avoid decimals

1. He starts with orange juice to lemonade in the ratio 4:16 (This adds up to 20)
2. He drinks 1/4, leaving 3/4 of each amount of substance.
In this case, 3/4 of 4 is 3, and 3/4 of 16 is 12. The new ratio is 3:12 (This adds up to 15)
3. 20 - 15 = 5, he fills this remaining glass up with orange juice. 3 + 5 = 8, so now the ratio is 8:12.
4. Simplify to 2:3
Hope it helps, and please tell me if I'm wrong
2
#6
I found out the remaining quantities and got 1 mark
Then I understood that you can replace each ratio with the quantity and that's where my answer stopped being right.
(Original post by Muttley79)
So what did you try?
0
2 years ago
#7
(Original post by sunnyday420)
Let use turn the ratio 1:4 to 4:16 for ease and to avoid decimals

1. He starts with orange juice to lemonade in the ratio 4:16 (This adds up to 20)
Edit your post - you are breaking the forum rules!
Last edited by Muttley79; 2 years ago
0
2 years ago
#8
(Original post by NelsaH)
I have had a go and I got completely the wrong answer and basically guessed how to do it...

I found out the remaining quantities and got 1 mark
Then I understood that you can replace each ratio with the quantity and that's where my answer stopped being right.
Can you post what you did please?
0
#9
Thanks!
You have been really helpful! very Grateful
(Original post by sunnyday420)
Let use turn the ratio 1:4 to 4:16 for ease and to avoid decimals

1. He starts with orange juice to lemonade in the ratio 4:16 (This adds up to 20)
2. He drinks 1/4, leaving 3/4 of each amount of substance.
In this case, 3/4 of 4 is 3, and 3/4 of 16 is 12. The new ratio is 3:12 (This adds up to 15)
3. 20 - 15 = 5, he fills this remaining glass up with orange juice. 3 + 5 = 8, so now the ratio is 8:12.
4. Simplify to 2:3
Hope it helps, and please tell me if I'm wrong
0
2 years ago
#10
(Original post by sunnyday420)
Let use turn the ratio 1:4 to 4:16 for ease and to avoid decimals

1. He starts with orange juice to lemonade in the ratio 4:16 (This adds up to 20)
2. He drinks 1/4, leaving 3/4 of each amount of substance.
In this case, 3/4 of 4 is 3, and 3/4 of 16 is 12. The new ratio is 3:12 (This adds up to 15)
3. 20 - 15 = 5, he fills this remaining glass up with orange juice. 3 + 5 = 8, so now the ratio is 8:12.
4. Simplify to 2:3
Hope it helps, and please tell me if I'm wrong
I like the way you answered the question. I wouldn’t have thought to to the ratio into 4:16 for ease. Cool method.
0
2 years ago
#11
Huh? am I not allowed to help?
(Original post by Muttley79)
Edit your post - you are breaking the forum rules!
0
2 years ago
#12
(Original post by sunnyday420)
Huh? am I not allowed to help?
Doing the question is not 'helping' - we just give a hint - please read the rules before posting again 0
2 years ago
#13
I recently done this question. The answer was 2:3 from what I remember
1:4 x 4 = 4:16
He drinks a 1/4 therefore you x each side of the ration by 3/4 which gives you 3:12
He is now at 3/4 of a cup of liquid
4+16 = 20 and since we need a 1/4 20 x 0.25 = 5
You add 5 to the 3 on the left as this is orange juice
The ratio is now 8:12
Divide both sides by 4
2:3
Hope it helps!
(Original post by NelsaH)
I have read the mark scheme but I do not understand why the steps are done!
would appreciate a step by step guide for this question thanks!

Ben fills a glass with orange juice and lemonade in the ratio 1 : 4 by volume. He mixes the liquid that is in the glass.
Ben drinks 1/4 of this liquid. He then fills the glass using orange juice. Work out the ratio of orange juice to lemonade, by volume, that is now in the glass. Give your ratio in its simplest form.
0
#14
1:4 is 1/5 : 4/5 (1mark)
so..
1-1/4 : 4-1 which is 3/4 : 3 (1 mark)
and then I did 3 multiplied by 4/5 and that was 12/5 and I left the ratio as 12/5 : 4/5...….
(Original post by Muttley79)
I found out the remaining quantities and got 1 mark

Can you post what you did please?
0
2 years ago
#15
(Original post by sunnyday420)
Let use turn the ratio 1:4 to 4:16 for ease and to avoid decimals

1. He starts with orange juice to lemonade in the ratio 4:16 (This adds up to 20)
2. He drinks 1/4, leaving 3/4 of each amount of substance.
In this case, 3/4 of 4 is 3, and 3/4 of 16 is 12. The new ratio is 3:12 (This adds up to 15)
3. 20 - 15 = 5, he fills this remaining glass up with orange juice. 3 + 5 = 8, so now the ratio is 8:12.
4. Simplify to 2:3
Hope it helps, and please tell me if I'm wrong
I got the same thing, I did it a different way tho,
I gave a value to the amount of liquid (120) and then applied the ratio to it ( any value can be taken, 120 was just easy to work with)
1:4 = 5
24: 96 = 120
120 * 3/4 = 90 ( a fourth was drunk)
1:4 = 5
18: 72 = 90
added value to the amount of orange juice to make it the same amount as before ( a glass of 120ml as seen at the top)
as a fourth of the glass was taken, (30ml, that's the amount of orange juice that will have to be added to the glass to fill it to the top again)

so
18 + 30 = 48
48 + 72 = 120
48:72 which simplifies to 2:3
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