- Bossimbacon

Shawn ran 5 miles more than Alex ran. The sum of their distances is 19 miles. How far did Alex run? The domain of the solution is {7, 12, 14, 24}.
Grading Rubric
2 points: Choose a letter to represent your unknown value
2 points: Write an algebraic expression for each person using only one variable
2 points: Write an equation using the two algebraic expressions
2 points: Plug in each value from the domain into the equation
2 points: Find the distance Alex ran
Can anyone help me pls?

- katieb

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- Haseeb96

what do u think so, what is the correct answer ?

- Bossimbacon

well I dont quite understand the question and theres many questions to it could you guide me through it? @Haseeb96

- jim_thompson5910

`Choose a letter to represent your unknown value`
which letter do you want to pick?

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## More answers

- Bossimbacon

any letter will be fine?

- jim_thompson5910

yeah, usually x works

- Bossimbacon

ok
then x

- jim_thompson5910

`Shawn ran 5 miles more than Alex ran`
if Alan ran x miles (some unknown number of miles), then how many did Shawn run? in terms of x

- Bossimbacon

s5+a?

- Bossimbacon

i dont know haha

- jim_thompson5910

where are you getting s and a?

- jim_thompson5910

let's use actual numbers
say Alan ran 7 miles
how many miles did Shawn run?

- Bossimbacon

12

- jim_thompson5910

how did you get that

- Bossimbacon

cause it saids shawn ran 5 more miles than alan

- jim_thompson5910

so you basically add 5 to whatever Alan has
if Alan has x, then shawn has x+5

- Bossimbacon

ooooohhh

- jim_thompson5910

adding x to x+5 gives what?

- Bossimbacon

5x?

- jim_thompson5910

1apple + 1apple = 2apples
so x+x = 2x

- jim_thompson5910

x + x+5 would turn into 2x+5, right?

- Bossimbacon

yeah

- jim_thompson5910

`The sum of their distances is 19 miles`
we just found the total distance to be 2x+5
equate the two
2x+5 = 19
then solve for x

- Bossimbacon

x would be 7 @jim_thompson5910

- jim_thompson5910

good

- jim_thompson5910

and x+5 would be x+5=7+5 = 12
so Alan ran 7 miles, Shawn ran 12 miles
7+12 = 19 checks out

- Bossimbacon

but does this answer each question?
2 points: Choose a letter to represent your unknown value
2 points: Write an algebraic expression for each person using only one variable
2 points: Write an equation using the two algebraic expressions
2 points: Plug in each value from the domain into the equation
2 points: Find the distance Alex ra

- jim_thompson5910

how did you find that x = 7

- jim_thompson5910

did you plug in various x values? or did you isolate x?

- Bossimbacon

plug in

- jim_thompson5910

so you did the `Plug in each value from the domain into the equation` step. Be sure to list every value from that set

- Bossimbacon

oh no i didnt ill make sure to put that in thank you! but what about the other questions?

- Bossimbacon

2 points: Write an algebraic expression for each person using only one variable?

- jim_thompson5910

that's when I said that
alan ran x miles
shawn ran x+5 miles

- Bossimbacon

Write an equation using the two algebraic expressions

- Bossimbacon

what about this question? Write an equation using the two algebraic expressions

- jim_thompson5910

I wrote the equation above too

- Bossimbacon

@jim_thompson5910 thank you so much! really means alot! I appreciate your patience :)

- jim_thompson5910

you're welcome

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