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Arjun and Gretal each pay rent. In 2018, the ratio of the amount each paid in rent was Arjun : Gretal In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 5:7. = 9:13. Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019.​

User Saad Anees
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1 Answer

8 votes

Answer:

$6525

Explanation:

I rewrote the problem before because the ratios are not clear in the given problem.

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Arjun and Gretal each pay rent.

In 2018, the ratio of the amount each paid in rent was Arjun:Gretal=5:7.

In 2019, the ratio of the amount each paid in rent was Arjun:Gretal=9:13.

Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019.​

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2018: Arjun/Gretal = 5x/7x

2019: Arjun/Gretal = 9y:13y

5x = 9y

13y = 7x + 290

Solve the first equation for x. Substitute in second equation.

x = 9y/5

13y = 7(9y/5) + 290

Multiply both sides by 5.

65y = 63y + 1450

2y = 1450

y = 725

In 2019, Arjun's rent was 9y.

9y = 9(725) = 6525

Answer: $6525

Check:

Solve for x.

x = 9y/5 = 9(725)/5 = 1305

Now we find Arjun's and Gretal's rents in both 2018 and 2019.

2018: Arjun 5x = $6525; Gretal 7x = $9135

2019: Arjun 9y = $6525; Gretal 13y = $9425

Arjun's rent is the same in both 2018 and 2019 as the problem states.

Gretal's rent is $290 more in 2019 than in 2018 since $9425 - $9135 = $290.

This confirms the answer $6525 is correct.

User Jasper Siepkes
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