Rony spent 20% of his salary on a wallet. He bought a bag which cost $20 more than the wallet. He also bought a pair of shoes. The ratio of the cost of the wallet to the cost of the pair of shoes was 5:6. He then had $844 left.
(a) What was his monthly salary?
(b) Express the amount of money he spent on the pair of shoes as a fraction of his monthly salary in its simplest form.
(a) His monthly salary was $4,220.
(b) He spent $672 on the pair of shoes, which is 16/25 of his monthly salary.
Let's use algebra to solve this problem. Let R be Rony's monthly salary.
(a) We know that Rony spent 20% of his salary on a wallet, so he spent 0.2R on the wallet. We also know that the bag cost $20 more than the wallet, so he spent 0.2R + $20 on the bag. Let S be the cost of the shoes. We are given that the ratio of the cost of the wallet to the cost of the shoes was 5:6, so we can write:
0.2R/5 = S/6
Simplifying this equation, we get:
0.04R = S/6
Multiplying both sides by 6, we get:
0.24R = S
We also know that Rony had $844 left after buying the wallet, bag, and shoes. Therefore:
R - 0.2R - (0.2R + $20) - S = $844
Simplifying this equation and substituting 0.24R for S, we get:
R - 0.44R - $20 - 0.24R = $844
Simplifying further, we get:
0.32R = $864
Dividing both sides by 0.32, we get:
R = $2400
Therefore, Rony's monthly salary was $2400.
(b) We know that Rony spent 0.2R on the wallet and 0.2R + $20 on the bag. Therefore, he spent a total of 0.4R + $20 on the wallet and bag. We also know that he spent 0.24R on the shoes. Therefore, he spent a total of 0.4R + $20 + 0.24R on the wallet, bag, and shoes. We are asked to express the amount of money he spent on the shoes as a fraction of his monthly salary. We can write:
0.24R / R = 0.24
Simplifying this fraction, we get:
0.24 = 24/100 = 6/25
Therefore, the amount of money Rony spent on the shoes was 6/25 of his monthly salary.
So, he spent 6/25 of $2400, which is $576. We can also express this as a percentage by multiplying by 100, which gives us 24%. Therefore, Rony spent 24% of his monthly salary on the pair of shoes.
To solve this problem, let's break it down step by step.
(a) Let's assume Rony's monthly salary is S dollars.
Rony spent 20% of his salary on a wallet, which means he spent 0.2S dollars.
He bought a bag that cost $20 more than the wallet, so the cost of the bag is 0.2S + $20.
The total amount spent on the wallet and bag is 0.2S + (0.2S + $20) = 0.4S + $20.
Out of his salary, Rony also bought a pair of shoes. The ratio of the cost of the wallet to the cost of the pair of shoes is 5:6.
Let's assume the cost of the wallet is 5x dollars and the cost of the shoes is 6x dollars.
According to the ratio, we have:
5x + 6x = 0.4S + $20
Combining like terms, we get:
11x = 0.4S + $20
Rony also had $844 left after purchasing these items. This means that the amount spent is equal to the salary minus $844:
0.4S + $20 + 5x + 6x = S - $844
Simplifying the equation, we have:
11x + 0.4S = S - $824
Now, our goal is to solve for S, Rony's monthly salary. To do this, let's isolate S on one side of the equation:
0.4S - S = -$824 - 11x
-0.6S = -$824 - 11x
-0.6S = -11x - $824
0.6S = 11x + $824
S = (11x + $824) / 0.6
So, the formula for Rony's monthly salary is S = (11x + $824) / 0.6.
(b) Now let's find the fraction of his monthly salary that he spent on the pair of shoes.
The amount spent on the shoes is 6x dollars, and his monthly salary is S dollars.
To express the amount spent on shoes as a fraction of his monthly salary, we divide the amount spent on shoes by his monthly salary and simplify it.
The fraction is: (6x / S)
Please note that we cannot simplify this fraction further without knowing the specific values for x and S.