Answer:
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
