Destinie Jones

2022-08-12

let c be the distance between Carlisle and Wellesley ,let b be the distance between Carlisle and Stonebridge, let a be the distance between Wellesley and Stonebridge. if you did a circuit, traveling from Carlisle to Wellesley to Stonebridge  and back to Carlisle you would travel 73 miles. the distance from Stonebridge to Carlisle is 12 miles farther than the distance from Wellesley to Carlisle. if you drove from Stonebridge to Carlisle and back to Stonebridge and then continue to Wellesley then back to Stonebridge you would travel 102 mile.

1.write a system of linear equations to represent the situation

2. solve the system of equations. explain the meaning of the solutions in the context of the situations.

Jeffrey Jordon

A)

Let the three places are denoted by S, C and W respectively.

According to question, a,c,b are the distances between Stonebridge(S) & Carlisle(C), Carlisle(C) & Wellesley (W)and Welleslay(W) & Stonebridge(S) respectively.

Now,

Since if we travel C to W to S to C to C then it is equal to 73miles.

So,

c + a + b = 73 .....(1)

Since distance between S and C is 12 miles father than distance between W and A.

So, b = 12 + c .....(II)

Or c = b - 12 ....(2)

Since if we drove S to C and back to S and than to W and back to S, the total travelling is 102 miles.

So, b + b + a + a = 102

Or 2b + 2a = 102 .....(II)

On dividing both sides by 2, we get

b + a = 51 .....(III)

Or a = 51- b ....(3)

Hence, the equation (I), (II) and(III) are the system of equations that represents the given situation.

(A)

On Putting the values of c and a from equations (2) and (3) in equation (1), we get

b - 12 + 51- b + b = 73

b +39 = 73

Or b = 73 - 39 = 34 miles ....(4)

On putting b =136 miles in equation(2) and (3) , we get

c = b - 12 = 34 - 12 = 22 miles ...(5)

and

a = 51 - 34 = 17 miles ...(6)

Hence, a = 17 miles, b = 34 miles, c = 22 miles

Here, This solution means that the distance between

●Wellesley and Stonebridge is a = 17 miles

●Stonebridge and Carlisle is b = 34 miles

●Carlisle and Welleslay is c = 22 miles

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