Question

Arjun and Greta each pay rent

in 2018, the ratio of the amounts payed was Arjun:gretal 5:7
In 2019, the ratio of the amount each paid in rent was Arjun : Gretal 9:133

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.

Answer 1

Given :- Arjun and Gretal each pay rent in 2018, the ratio of the amounts payed 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.

Answer :-

Let us assume that,

• Arjun paid in 2018 = $ 5x
• Gretal paid in 2018 = $ 7x
• Arjun paid in 2019 = $ 9y
• Gretal paid in 2019 = $ 13y .

given that,

→ 5x = 9y -------- Eqn.(1)

→ 7x + 290 = 13y

→ 13y - 7x = 290 ------ Eqn.(2)

putting value of x from Eqn.(1) in Eqn.(2),

→ 5x = 9y

→ x = (9y/5) .

so,

→ 13y - 7(9y/5) = 290

→ 13y - (63y/5) = 290

→ (65y - 63y) / 5 = 290

→ 2y = 290 * 5

→ y = $725 .

therefore,

→ Amount Arjun paid in rent in 2019 = 9y = 9 * 725 = $6525 (Ans.)

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Answer 2

Answer:

$6525

Step-by-step explanation:

2018: Arjun to Gretal is 5:7
2019: Arjun to Gretal is 9:13

since Arjun paid the same amount of rent in both years, so we make 5 and 9 to 45.
in 2018: 5x9 :7x9 ==> 45:63
in 2019: 9x5 : 13x5 ==> 45:65

So there are 2 parts difference for Gretal which equal to $290
2 parts - $290
1 part - $145

so 45 x $145 = $6525