Fraction worded problem about salary and spending

[MathsFormula]

Steve spends his income as follows :

2/5 of his income goes on tax.

2/3 of what is left goes on food and rent.

The rest he spends on beer and gambling.

QUESTION: What fraction of his income is spent on beer and gambling?

ANSWER IN BOOK IS 1/5


My calculation gives the wrong answer. Here's my attempt:

2/5 is TAX so 3/5 is CASH to spend.

2/3 of the CASH is spent on food and rent so 2/3*3/5 = 2/3. So 2/3 spent on food and rent.

So 1/3 remains for beer and gambling.

The fraction of the income is (1/3)/(3/5) = 5/9

WRONG ANSWER.

Please help. Thank you

 

[stapel]

Steve spends his income as follows :

2/5 of his income goes on tax.

2/3 of what is left goes on food and rent.

The rest he spends on beer and gambling.

QUESTION: What fraction of his income is spent on beer and gambling?

ANSWER IN BOOK IS 1/5


My calculation gives the wrong answer. Here's my attempt:

2/5 is TAX so 3/5 is CASH to spend.

2/3 of the CASH is spent on food and rent so 2/3*3/5 = 2/3.

How are you getting that (2/3)(3/5) equals 2/3? Since 3/5 does not equal 1, then how can multiplying by 3/5 leave you with what you'd started with?

 

[Harry_the_cat]

Steve spends his income as follows :

2/5 of his income goes on tax.

2/3 of what is left goes on food and rent.

The rest he spends on beer and gambling.

QUESTION: What fraction of his income is spent on beer and gambling?

ANSWER IN BOOK IS 1/5


My calculation gives the wrong answer. Here's my attempt:

2/5 is TAX so 3/5 is CASH to spend.

2/3 of the CASH is spent on food and rent so 2/3*3/5 = 2/3. So 2/3 spent on food and rent. Check this calculation!

So 1/3 remains for beer and gambling.

The fraction of the income is (1/3)/(3/5) = 5/9

WRONG ANSWER.

Please help. Thank you

See red comments.

 

[Johulus]

Steve spends his income as follows :

2/5 of his income goes on tax.

2/3 of what is left goes on food and rent.

The rest he spends on beer and gambling.

QUESTION: What fraction of his income is spent on beer and gambling?

ANSWER IN BOOK IS 1/5


My calculation gives the wrong answer. Here's my attempt:

2/5 is TAX so 3/5 is CASH to spend.

2/3 of the CASH is spent on food and rent so 2/3*3/5 = 2/3. So 2/3 spent on food and rent.

So 1/3 remains for beer and gambling.

The fraction of the income is (1/3)/(3/5) = 5/9

WRONG ANSWER.

Please help. Thank you

That was a good start. \(\displaystyle \dfrac{2}{5} \) is spend on tax so it's left: \(\displaystyle 1-\dfrac{2}{5}=\dfrac{3}{5} \). \(\displaystyle \dfrac{2}{3} \) of cash that is left ( \(\displaystyle \dfrac{3}{5} \)) is spent on food and rent. You wrote \(\displaystyle \dfrac{2}{3}\cdot \dfrac{3}{5} \) which is good, but your answer came out wrong. It's not \(\displaystyle \frac{2}{3} \). Try to calculate \(\displaystyle \dfrac{2}{3}\cdot \dfrac{3}{5}=x \) again, and if you have problems try pluging it in a calculator and you will see what you get. Do you know how fractions are multiplied? Numerator's are multiplied one with another and denominator's are multiplied one with another. And after that you can simplify the fraction if numerator and denominator are both divisible by the same number. You see that amount of income that is spent on certain things is marked by fractions. How would you then mark the whole amount of income? Imagine we have apple and we divide it in four parts. We would have four quarters. How would you mark one part of an apple mathematically(it's one quarter of an apple). What do you get when you sum up all parts of an apple that you got?(i.e. when you sum up four quarters, what do you get?). It is the same with income in this task. It is divided in fractions. So, if you understood what I was trying to say with example about an apple, you should be able to understand this task now. All you have to do is subtract all fractions of cash that are spent on other things from the whole amount of income. And that is why is important to know how to mark the total amount of income.

 

[MathsFormula]

Thanks for all the help. Finally got it using the symbol X

I'll show you all so that you can tell me if it's okay or not. Also did it as SALARY = 1 because using X seems overboard on this basic arithmetic question.

Method ONE:

Let salary be X

2/5 of income is tax so 3/5 of income is CASH

3/5 of income means 3/5*X = 3/5X is CASH

2/3 of what is left is spent on food leaving 1/3 for beer.

So for beer that is 1/3 * 3X/5 = 3X/15 = X/5

Fraction of the income is (X/5)/X = 1/5
CORRECT ANSWER


METHOD TWO

LET INCOME = 1
2/5 of income is tax so 3/5 of income is CASH

3/5 of income means 3/5*1 = 3/5 is CASH

2/3 of what is left is spent on food leaving 1/3 for beer


So for beer that is 1/3 * 3/5 = 3/15 = 1/5