Question

thea visited her grandparents in the farm. the ratio of the chicken to ducks is 7:4. the difference is 15. how many chickens and how many ducks are there?

Answer 1

....x= hens

y = ducks

the ratio between hens and ducks is 7:4--->x/y = 7/4

the difference is 15--->x-y=15

system :

x/y=7/4--->4x=7y

x-y=15

rewrite the system

4x-7y=0

x-y=15

by substitution: x=15+y

replace x in the other equation

4(15+y)-7y=0

60+4y-7y=0

-3y=-60

3y=60

y = 20

there are 20 ducks

we calculate x:

x-y=15

x-20=15

x=15+20

x=35

there are 35 hens

check:

the ratio between hens and ducks is 7:4

35 hens, 20 ducks

ratio 7:4 = 35/20=7:4