Question

Bernard is two years older than his sister Therese and four years younger than his sister

Josephine. The product of his sisters' ages is the age of his mother, 40.

A. If x is Bernard's age, write his two sisters' ages in terms of x.
Answer:

B. Write Bernard's mother's age in terms in terms of x and solve this quadratic equation.

Answer:


C. What is Bernard's age?
Answer:


Please show working out​

Answer 1

Firstly Bernard = x

A) lets focus on Therese first. Bernard id two years older than her so for Therese’s equation in terms of x it would be x+2. Now for Josephine Bernard is 4 years younger than HER so it would be 4-x.

B) The mother is the PRODUCT of the sisters’ ages so (multiplication)

It would be like this: (x+2)(4-x)= 40 This is all in terms of x.

Solving for the equation (using distributive property) we get:

4x-x+8-2x=40

(Reorganize to group like terms, remember to go in order from the numeral numbers with variables, to variables only then numbers only): 4x-2x-x+8=40 (now combine like terms and simplify): x+8=40 this is his mom’s age in terms of x

C) HERE we can solve for x:

Isolating x to get the answer we move the 8 to the other side of the equation and it becomes a negative 8 so:

x=40-8

x=32

Therefore Bernard is 32 years old.

Hope this helps!