# pls help (1 Viewer)

#### mathsbrain

##### Member
Question: Sugar is dissolved in water in the ratio 1:3 to form sugar syrup. This sugar syrup is further diluted with the addition of water so that the ratio of the sugar syrup to the additional water is 5:7. FInd the ratio of sugar to water in the final mixture.

#### Accurate

##### clix
1/4 times 5/12 = 5/48 (that's how much sugar there is )

the rest is water so 43 (48-5)

I think the answer is 5:43

uh i think i got this wrong though, but i guess this is my quick attempt

edit : its right somehow

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#### Drdusk

##### π
Moderator
$\bg_white \text{I did this in a bit of a rush but here}$

$\bg_white \text{Let the amount of syrup be 'q', and the amount of initial water be 'r'. Also let the amount of water added be 'x'}$

$\bg_white \therefore \frac{q}{r} = \frac{1}{3},\hspace{2mm} \frac{q + r}{x} = \frac{5}{7}$

$\bg_white \text{We are required to find the value of } \frac{q}{r + x} \text{as (r + x) equals the total amount of water at the end and q is the amount of sugar}$

$\bg_white \frac{q+ r}{x} = \frac{5}{7}\Rightarrow x = \frac{7(q + r)}{5}\text{. Subbing this into q/(r+x) gives}$

$\bg_white \frac{q}{r+x} = \frac{q}{r + \frac{7(q + r)}{5}} = \frac{5q}{5r + 7(q + r)}$

$\bg_white \text{Multiplying top and bottom by 1/q gives:}$

$\bg_white \frac{5q}{5r + 7(q+r)} = \frac{5q}{5r + 7(q+r)} \times \frac{1/q}{1/q} = \frac{5}{\frac{5r}{q} + 7(q+r)/q} = \frac{5}{(5r/q) + 7(1 + r/q)}$

$\bg_white \text{Now from our first equation we have:}\hspace{2mm} \frac{q}{r} = \frac{1}{3}\Rightarrow \frac{r}{q} = 3$

$\bg_white \therefore \hspace{2mm} = \frac{5}{5(3) + 7(1+3)}$

$\bg_white = \frac{5}{43}$

$\bg_white \therefore \text{The ratio is}\hspace{2mm} 5:43$

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5:43 ?

#### idkkdi

##### Active Member
If we let original value be 1000mL.

Amount of sugar = 1000 x 1/4 = 250mL, Amount of water = 1000 x 3/4 = 750mL

5:7 ratio sugar with additional water.

1000L x 7/5 = 1400mL additional water.

250: 2150
5:43

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#### Accurate

##### clix
If we let original value be 1000mL.

Amount of sugar = 1000 x 1/4 = 250mL, Amount of water = 1000 x 3/4 = 750mL

5:7 ratio sugar with additional water.

250mL x 7/5 = 350mL additional water.

250mL: 750mL+350mL
250:1100
5:22
Well using your same method I got 5:43

Let total be 1000ml

250:750 = 1:3

1000:1400 = 5:7

To calculate how much water there is we know that 750ml of that original 1000ml is water, plus add another 1400ml of water so a total of 2150 ML

There is 250 grams of sugar in the solution so 250:2150

= 5/43

5:43

#### Accurate

##### clix
They added extra water to the original solution not another mixture

#### idkkdi

##### Active Member
My bad, didn't notice sugar SYRUP.

#### AJ_264

##### New Member
God is always the answer.

#### Drdusk

##### π
Moderator
Its 5:43 confirmed by my 4u state ranking friend haha.
I made a silly error when I said q/(x) = 5/7. It's actually (q+r)/x = 5/7

This should get you 5:43

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#### idkkdi

##### Active Member
Isn't 48 including sugar?

Moderator