How to solve this ratio problem using algebra

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Tygra

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Dear, all,

I have this ratio problem:

A man who smokes 15 cigarettes a day, find that 24 packets last him 32 days. If he cuts down to only 12 cigarettes a day, and buys 18 packets, how long will they last?

Could someone help me solve this algebraically?

Many thanks.
 
Tygra said:
Dear, all,

I have this ratio problem:

A man who smokes 15 cigarettes a day, find that 24 packets last him 32 days. If he cuts down to only 12 cigarettes a day, and buys 18 packets, how long will they last?

Could someone help me solve this algebraically?

Many thanks.
Click to expand...
Please post your attempt. Or an example you went through that uses ratios and algebra.
 
Well I know how to solve it without using algebra. Its just:

32*(5/4)*(3/4) = 30 days

I'm not sure if it can be solved using algebra. This question has been a bogey question for me even though I am far passed GCSE level. I am about to start tutoring maths at GCSE and came back to this question from years ago, and wondered if there was any algebraic way to solve it?
 
Tygra said:
Well I know how to solve it without using algebra. Its just:

32*(5/4)*(3/4) = 30 days

I'm not sure if it can be solved using algebra. This question has been a bogey question for me even though I am far passed GCSE level. I am about to start tutoring maths at GCSE and came back to this question from years ago, and wondered if there was any algebraic way to solve it?
Click to expand...
If "algebra" means variables and equations then you need to tweak your solution to use a variable and an equation. E.g. x is the number of days. And for the equation, equate the number of cigarettes per packet expressed using A. 15 cigarettes a day and B. 12 cigarettes a day.
 
I've got it!

Let P = number of cigarretes per packet
Let X = new numbers of days that they will last

eq1: P/15*24 = 32
eq2: P/12*18 = X

eq1: P = 32*15/24 = 20 (There are 20 cigarettes per packet)

Sub P into eq2:

eq2: X = 20/12*18 = 30

Thanks lev888 for prompting my brain to try what you said!
 
Tygra said:
I've got it!

Let P = number of cigarretes per packet
Let X = new numbers of days that they will last

eq1: P/15*24 = 32
eq2: P/12*18 = X

eq1: P = 32*15/24 = 20 (There are 20 cigarettes per packet)

Sub P into eq2:

eq2: X = 20/12*18 = 30

Thanks lev888 for prompting my brain to try what you said!
Click to expand...
This is not quite what I had in mind.
The number of cigarettes per packet is (32*15)/24 and it's also (x*12)/18. Solve for x.
 
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