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

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation:

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation: