Please tell me how to do this math question!?

Question

I have 450g of salt and flour mix. How many grams of flour should I add to reduce the percentage of salt in the mixture to 90% of what it was?
The answers are:
a) 50 b) 10 c) 30 d) 45 e) 60
Please answer "why" not just how as I am preparing for an exam and need to know how to do it in the future.
Thankyou for your help!

I have just copied out the question exactly from my math book.

Answer 1

Helmut's answer is the best so far, except that he's written 0.09 instead of 0.90 in a few places.

Several people don't seem to realise that the amount of salt is unknown, and not important.

Simply, if there are x grams of salt, the proportion of salt is x/450. If the new total mass is m, the proportion of salt will be x/m. For this to be 90% of the original proportion, we need x/m = 0.9 x / 450; the x's cancel and we get m = 450 / 0.9 = 500 g. So we need to add 500-450 = 50 grams of flour - or, indeed, of anything except salt - and we will have the right proportion.

Answer 2

The answer is a(50)

the key is to remember, the amount of salt in the mixture remain the same before and after.

lets assume the gram of salt in the mixture is A gram, and the amount of flour added is Z gram

A g / 450g = the percentage of salt in the mixture before adding anything.
they want to reduce the percentage of salt in the mixture to 90% of what it was. which the final salt percentage
= 90% (A g / 450g)

the percentage of salt after adding flour
= A g / (450g + Z g)


now we can make an equation:

90% (A g / 450g) = A g / (450g + Z g)

solve the equation, first, you can get rid of unknow A by multuplying 1/A on both side of the equation.

you should be able to solve the equation now and find out the number of Z is 50.

Answer 3

I am confused, and I have a feeling the question has been written incorrectly. You start out saying you have a MIX of 450g of salt and flour mix. Without knowing what the starting percent of the mix is you can not answer the question. I have a feeling you meant to say that you had 450g of salt, and you have flour to mix into it. How much to make the salt a 90% mix with flour. To do it simply, for every 100g of 90% mix you have 10grams of flour in it, as 90g + 10g = 100....
you have 4.5 hundreds X 10g flour = 45g flour total

To do any problem like this, and this is better for the more complicated problems, when dealing with relationships, especially in percents, try this...

10% of flour is to 100% of a mix, as WHAT% is to 450g mix
set it up like this, a box, and do the math criss cross in an X

10
--- X ---
100 450

You fill in what you know, and the blank corner is the answer you want. Diagonally, 10 X 450 = 4500.
The other diagonal, 100 X WHAT = 4500
The only answer can be 45 to make that true.

This works with anything you want to show as a relationship.

Answer 4

answer is d)45! why? simply get the 10% of 450g mixture of flour & salt.

Answer 5

let x = the amount of salt and y = the amount of flour added.
x / (450 + y) = .09x / 450
x(450) = .09x(450 + y)
450 = .09(450 + y)
450 = 405 + 0.9y
0.9y = 45
y = 50

Answer 6

i think a) 50 is the right answer.

450/(450+x)=0.9
suppose you put x grams of flour

Answer 7

(assuming that the salt and flour are of equal quantity)
x = 450g(total mass of the mix)
n = amount of flour to be added

225g = .5x
225g = .45(x + n)
225g = 202.5g + .45n
n = 50g

i think...

Answer 8

Please double check the original problem. To me it looks like you left out the part of what percent you were starting with in terms of salt.

Sorry.