Question

Margaret ran 2 more miles than Lynn. The sum of their distance is 20 miles.

(a) Define your variables.

(b) Write algebraic expressions for the distance each person ran.

(c) Write an equation that can help you solve the problem.

(d) How far did Margaret run?

(e) How far did Lynn run?

please help me solve all a-e :b

Answer 1

It is given in the question that

Margaret ran 2 more miles than Lynn. The sum of their distance is 20 miles.

a. Let Lynn runs x miles and Margaret runs y miles .

And them sum of their distances is 20 miles. That is

`x+y=20`

And it is given that Margaret runs 2 more miles than Lynn .

Therefore,we have

`y=x+2`

b. Algebraic expressions of the distances each person ran

`d_(Lynn) = x miles \\ d_(Margaret) = y miles`

c. So the equations are

`x+y=20 \\ y= x+2`

Substituting the value of y in first equation

`x+2+x =20 \\ 2x+2 =20 \\ 2x=18 \\ x = 9 miles`

e. THerefore Lynn run 9 miles.

d. Margreta run

`(9+2)= 11 miles`