five years ago, Agnes was 3 times as old as Valerie was. Next year Agnes will be twice as old as Valerie will be. How old are they now?

Agnes is 23 and Valerie is 11 now.

Step-by-step explanation:

a - Agnes's age

v - Valerie's age

a - 5 - Agnes's age five years ago

v - 5 - Valerie's age five years ago

and:

a - 5 = 3(v - 5)

a + 1 - Agnes's age next year

v + 1 - Valerie's age next year

and:

a + 1 = 2(v + 1)

so we have equation system:

{a - 5 = 3(v - 5)

{a + 1 = 2(v + 1)

{a - 5 = 3v - 15

{a + 1 = 2v + 2

{a = 3v - 10

{3v - 10 + 1 = 2v + 2

{a = 3v - 10

{3v - 2v = 2 + 10 - 1

{a = 3v - 10

{v = 11

{a = 3 · 11 - 10

{v = 11

{a = 33 - 10

{v = 11

{a = 23

{v = 11

We can check it:

- 5 years ago:

Agnes: 23 - 5 = 18

Valerie: 11 - 5 = 6

18 ÷ 6 = 3, so Agnes was 3 times as old as Valerie

- next year:

Agnes: 23 + 1 = 24

Valerie: 11 + 1 = 12

24 ÷ 12 = 2, so Agnes will be twice as old as Valerie

the answer to the question is a  

it has the same slope and the same y-intercept.

answer: was that a question or answer?

step-by-step explanation: