Question

Angie, Mark, Taylor, Kim and Paul recently discovered that all of their birthdays were on the same day. However,none of them are the same age.They threw a party to celebrate their birthdays and I happened to overhear someof their conversation:Angie to Mark: "I was born on your 17th birthday."Mark to Taylor: "I am older than you but younger than Kim."Taylor to Angie: "I am double your age."Mark to Angie: "I am double your age plus 2 years."Kim to Taylor:"My age is equivalent to your age plus Angie's age."Paul to Taylor: "My age is 60% greater than your age.How old is each person? Justify your answer.

Answer 1

From the conversations, we need to write equations that allow us to find each age.

Let's define the next variables:

A: Angie's age

M: Mark's age

T: Taylor's age

K: Kim's age

P: Paul's age

Angie to Mark: "I was born on your 17th birthday."

This means that Mark is 17 years older than Angie. Mathematically:

M = A + 17 (eq. 1)

Taylor to Angie: "I am double your age." Mathematically:

T = 2A (eq. 2)

Mark to Angie: "I am double your age plus 2 years." Mathematically:

M = 2A + 2 (eq. 3)

Kim to Taylor: "My age is equivalent to your age plus Angie's age." Mathematically:

K = T + A (eq. 4)

Paul to Taylor: "My age is 60% greater than your age." Mathematically:

P = 1.6T (eq. 5)

Combining equations 1 and 3:

A + 17 = 2A + 2

17 - 2 = 2A - A

15 = A

Substituting this result in equation 1:

M = 15 + 17

M = 32

Substituting A = 15 in equation 2:

T = 2x15

T = 30

Substituting A = 15 and T = 30 in equation 4:

K = 30 + 15

K = 45

Substituting T = 30 in equation 5:

P = 1.6x30

P = 48