The ratio of two numbers is 3:5. When 4 is subtracted from the lesser of the two numbers and 8 is added to the larger of the two, the new ratio is 2:7. What is the greater of the two numbers before 8 is added to it?

Question

Mathematics

Abigail Rivas

20 May, 16:17

The ratio of two numbers is 3:5. When 4 is subtracted from the lesser of the two numbers and 8 is added to the larger of the two, the new ratio is 2:7. What is the greater of the two numbers before 8 is added to it?

+5

Answers (1)

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Madilynn Foley · Answer 1

X and y

x:y=3:5

or

x/y=3/5

when 4 is subtracted from x and 8 is added to y new ratio is 2:7

(x-4) / (y+8) = 2/7

we have

x/y=3/5

(x-4) / (y+8) = 2/7

get rid o frationc

x/y=3/5

times both sides by 5y

5x=3y

(x-4) / (y+8) = 2/7

times both sides by 7 (y+8)

7 (x-4) = 2 (y+8)

7x-28=2y+16

add 28 both sides

7x=44+2y

we have

5x=3y

and

7x=2y+44

multiply first equation by 2 and seecond equaiton by 3

10x=6y and 21x=6y+132

sub 10x for 6y

21x=10x+132

minus 10x both sides

11x=132

divide both sides by 11

x=12

x/y=3/5

12/y=3/5

times both sides by 5y

60=3y

divide both sid esyb 3

20=y

12 and 20

the greater is 20