year 8 Maths Questions

[Mittleme]

could anyone please help

Question
A very large jug of x litres of orange squash is 10% concentrate(the rest water). When 5 litres of concentrate is added the jug is now is now 12% concentrate


a) form an equation in terms of x(by considering the amount of concentrate we have)
b) hence determine x

this is what ive done but not sure

x=10%
x+5 = 12%

thank you

[Mittleme]

Hi all

Please help with this Maths question for dd
Question
Skimmed Milk contains 0.1% fat and pasteurised whole milk contains 4% fat.
When 6 litres of skimmed milk are mixed with n litres of pasteurised whole milk, the fat content of the resulting mixture is 1.66%. what is n?

thank you

[Guest55]

Question
A very large jug of x litres of orange squash is 10% concentrate(the rest water). When 5 litres of concentrate is added the jug is now is now 12% concentrate

a) form an equation in terms of x(by considering the amount of concentrate we have)
b) hence determine x

This is a crazy question ... totally unrealistic

let amount of concentrate be c litres.

From first sentence c/x = 10/100 [10%] so 100c = 10x

Five litres of concentrate is added so we have c + 5 litres of concentrate and x + 5 litres altogether

c+ 5/(x + 5) = 12/100 100 (c + 5) = 12(x + 5)

100c + 500 = 12 x + 60 but we know 100x = 10x

10x + 500 = 12x + 60
440 = 2x so x = 220 litres [just think how big that really is]

Does that help you with the other one?

[solimum]

could anyone please help

Question
A very large jug of x litres of orange squash is 10% concentrate(the rest water). When 5 litres of concentrate is added the jug is now is now 12% concentrate


a) form an equation in terms of x(by considering the amount of concentrate we have)
b) hence determine x

thank you

The original x litres contains x/10 litres of concentrate and 9x/10 litres of water

the new jug contains (x/10) + 5 litres of concentrate and still only 9x/10 litres of water - total is now x + 5 litres altogether

if the new jug is 12% concentrated [x/10 + 5] / [x+5] = 12/100

or alternatively (multiplying both sides by [x+5] and by 100)

100*(x/10 + 5) = 12(x+5)

Multiplying out the brackets

10x + 500 = 12x + 60

Simplifying (subtract 10x from both sides, then subtract 60 from both sides)

440 = 2x

so x =220 litres

(that is a seriously ridiculous and unrealistic jug - who wrote this question? Should they be millilitres??)

Check: 220 litres at 10% means 22 litres concentrate

Add 5 litres means 27/225 = 0.12 or 12% - phew!

SNAP!! Guest55

[Surferfish]

For the milk question:

((6 x 0.1) + (n x 4)) / (6 + n) = 1.66

0.6 + 4n = 9.96 + 1.66n

Rearranging should give n = 4 litres. A bit more realistic than the other one!

[Mittleme]

Thank you All. just waiting for DD to sit down at the weekend and digest the solutions.

Many Thanks

[solimum]

Just as long as she doesn't try to digest 220 litres of orange squash!

[Guest55]

Please don't try to lift that many litres either