Linear system of equations

Question

Can you individually Calculate the two sisters' ages when Jane's and Nicole's ages add up to 32 while they are 6 years apart?

Hint: Both sisters are teenagers and use the fast-track method!

Answer 1

Given:

1. If we add t he two sisters Jane and Nicole's age it is equal to 32.
2. The difference between their age is 6.

Let us solve now;

Assume Jane's age as X and Nicole's age as Y.

Let us write the equation based on the given conditions,

Equation 1: X+Y =32;

Equation 2: X-Y = 6;

Now, let us solve these equation for x

Add equation 1 and 2

X+Y =32

X- Y=6

------------------

the Y get cancelled .

So 2X=38

divide by 2 on both side of the equation

2X 38

----- = ------

2 2

X = 19 ----- Jane's age is 19.

Now let us find Nicole's age.

Substitute X= 19 in the equation 1.

19+Y=32

isolate the Y

Y= 32-19

Y=13

Nicole's Age is 13.

Both of them are in teenage . Their ages are 19 and 13.

Answer 2

A- Fast track solution to find the older sister's age:

1-Add up their age sums with their age differences:

32+6 =38, then

2- Divide the result by 2, 38/2 =19 years is the older sister's age. This approach is the fast track to find the older sibling's age.

B- Fast-track solution to find the younger sister's age:

1- Calculate the difference between their age sums and their age gap:

32-6 =26, then

2- Divide the result by 2, 26/2=13 years is the younger sister's age.

OPTIONAL LONG TRACK METHOD by Linear system of equations:

Jane + Nicole = 32 ---> J +N = 32 [equation 1]

Jane - Nicole = 6 ----> J - N = 6 [equation 2]

then

J + N =32

J - N = 6

__________Add eq 1 + eq 2

2J +N - N = 38

2J+0 = 38 ; hence, J= 38/2=19, Jane's, older sister's age.

then

N = J -6 = 19-6 = 13 is the younger Nicole's age

Verify by: 19+13= 32, yes their age sum is 32 years.

Answer 3

Let J = Jane's age and N = Nicole's age

Assuming that Jane is older than Nicole, we have:

J + N = 32

J = N + 6

So, (N + 6) + N = 32

2N = 26

So, N = 13 and J = 19.

Nicole is 13 and Jane is 19.