Question

Emily spent 2/11 of her monthly salary on food,3/8 of the remaining on rent and 1/9 of what still remained on books .If she still had $200 left, find her salary per month ​

Answer 1

Given :

• The part of Salary Emily spends on food = 2/11
• The part of her salary she pay for the rent = 3/8
• The part of her salary she spend on books = 1/9
• Left money with her after overall spent money= $200

To find :

• Emily's monthly salary

Solution :

Let her monthly salary be ,'x'.

ATQ,

Money she spends on her food items = 2x/11

Money remains with her after buying food = x -2x/11 = 9x/11

Money she pays as rent = (3/8)*(9x/11) = 27x/88

Money remaining with her after paying rent = [x-(2x/11)-(27x/88)] = x(1-(2/11)-(27/88) = x[(88-16-27)/88] = 45x/88

Money she spends on her books = 1/9*45x/88 = 45x/9*88 =5x/88

Money left with her after all of the above listed payments = x-(2x/11)-(27x/88)-(5x/88) = x[(88-16-27-5)/88] =40x/88 = 5x/11

As mentioned,

• 5x/11 = 200
• 5x = 200*11
• 5x = 2,200
• x = 2,200/5
• x = $440

Therefore, Emily's salary per month would be equal to $440.

Answer 2

$440

Explanation:

Given information:

• Emily spent 2/11 of her monthly salary on food.
• Then she spent 3/8 of the remaining amount on rent.
• Then she spent 1/9 of what still remained on books.
• Emily had $200 left after all these expenses.

Let "x" be Emily's monthly salary.

If she spent 2/11 of her monthly salary on food, the amount left of her monthly salary is:

`\left(1-(2)/(11)\right)x=(9)/(11)x`

She then spent 3/8 of the remaining amount on rent, so she had 5/8 left of the remaining amount:

`(9)/(11)x \cdot (5)/(8)=(45)/(88)x`

She then spent 1/9 of what still remained on books, so she had 8/9 left of the remaining amount:

`(45)/(88)x \cdot (8)/(9)=(360)/(792)x=(5)/(11)x`

We are told that the amount she still had left is $200. Therefore:

`(5)/(11)x=200`

To find Emily's monthly salary, solve the equation for x:

`\begin{aligned}(5)/(11)x\cdot 11&=200\cdot 11\\\\5x&=2200\\\\(5x)/(5)&=(2200)/(5)\\\\x&=440\end{aligned}`

Therefore, Emily's monthly salary is $440.

We can check this by calculating her expenses.

Emily spent 2/11 of her monthly salary on food.

`\textsf{Food}=(2)/(11)\cdot \$440=\$80`

`\textsf{Remaining}=\$440-\$80=\$360`

Therefore, Emily spent $80 on food, and had $360 remaining.

She then spent 3/8 of the remaining amount on rent:

`\textsf{Rent}=(3)/(8)\cdot \$360=\$135`

`\textsf{Remaining}=\$360-\$135=\$225`

Therefore, Emily spent $135 on food, and had $225 remaining.

She then spent 1/9 of the remaining amount on books:

`\textsf{Books}=(1)/(9)\cdot \$225=\$25`

`\textsf{Remaining}=\$225-\$25=\$200`

Therefore, Emily spent $25 on books, and had $200 remaining.

Hence confirming that Emily's salary per month is $440.