Question

Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years. Set up the two equations that can be used to find each of their ages. Constraint 1: The solution must satisfy the ratio of their ages. Constraint 2: The solution must satisfy the sum of their ages. Only constraint would be met if Mrs. Lang is 32 and Jill is 8. Only constraint would be met if Mrs. Lang is 45 and Jill is 15.

Answer 1

Answer:

The two equations that can be used to find each of their ages are $x=4 \times y$ and $x+y=60$ .

Step-by-step explanation:

We are given that Mrs. Lang is 4 times as old as her daughter Jill. The sum of their ages is 60 years.

Let the age of Mrs. Lang be 'x years' and the age of her daughter Jill be 'y years'.

Now, according to the question;

• The first condition states that Mrs. Lang is 4 times as old as her daughter Jill, that means;

                                     $x=4 \times y$   ----------------- [equation 1]

• The second condition states that the sum of their ages is 60 years, that means;

                                 $x+y=60$

                                $4y + y = 60$     {using equation 1}

                                  $5y=60$

                                   $y=\frac{60}{5}$

                                   y = 12 years

Now, putting the value of y in equation 1 we get;

                               $x=4 \times y$

                               $x= 4 \times 12$ = 48 years

Hence, the age of Mrs. Lang is 48 years and her daughter Jill is 12 years old.