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.