(a) His monthly salary was $4,220.
(b) He spent $672 on the pair of shoes, which is 16/25 of his monthly salary.
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.
3 answers
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.
(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.