Answer:
Tamara is 5 years old.
Step-by-step explanation:
We can find Tamara's age by making expression in term of x. It is given that 1st sister is 7 years older and 2nd sister 3 years younger. So we can start making expressions :
Let x be Tamara's age,
Older sister,
x + 7
Younger sister,
x - 3
Given that the product of Tamara's ages is 24 which means you can multiply both of the sister together :
1st × 3rd = 24
(x+7)(x-3) = 24
x² - 3x + 7x - 21 = 24
x² + 4x - 21 = 24
Now, we have to solve the expression by factorisation :
x² + 4x - 21 = 24
x² + 4x - 45 = 0
(x+9)(x-5) = 0
x = -9(rejected)(age cannot be negative number)
x = 5
