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## 7th grade (Illustrative Mathematics)

### Unit 6: Lesson 1

Lesson 4: Reasoning about equations and tape diagrams (part 1)# Writing expressions word problems

CCSS.Math:

Learn how to write expressions with variables to describe situations described in word problems.

## Want to join the conversation?

- i still don't get it(25 votes)
- Word problem question: Go-cart rides cost $5. The go-cart operator takes in a total of $1000. How many times did people ride the go-carts in one day?(2 votes)
- At2:15, how do I know which unit to put as the numerator, and which unit to put as the denominator?

I keep getting questions wrong because of my placements.(2 votes) - So I have to write an equation?(2 votes)
- Hannah's school hosted a book donation. There are 150 students at her school, and they donated a total of books! Hannah donated 3 times as many as the average number of books each student donated.(1 vote)
- the difference of a number and 12(1 vote)
- Difference is subtract, and a number is any variable, so it would be x - 12(1 vote)

- There is a misconception in the first enigma. If the dentist fills any cavities then the victim has to pay 100 more dollars. Although later the inquest tells that he found n cavities but doesn't say that he filled those cavities. so does that not mean he only paid 50 dollars?(1 vote)
- I think it is more of an underlying assumption that the cavities will be filled as opposed to a misconception, but you are correct in that the patient does not have to have the cavities filled.(1 vote)

- Robbie, Jennie, Willie, and Kylie played a numbers game. Jennie picked a number but did not tell her friends. Robbie and Willie both picked a number as well, and Jennie described their numbers like this to Kylie.

Robbie picked a number that is nine more than four times Jennie's number.

Willie picked a number that is two less than three times Robbie's number.

Deciding to call her number, n, Jennie asked Kylie to write an expression that describes Willie's number.

Kylie came up with two expressions that equal Willie's number.

Her first expression was

(

n +

) - 2. Simplifying her first expression, her second expression was 12n +

.(1 vote) - how do you interpret single step algebraic expressions from a graph/sentence?

Thank you~ Sam McKenna(1 vote) - Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters.

How many pieces of jewelry did each sister receive?

Write your answer as an expression(1 vote)

## Video transcript

- [Voiceover] The price of a
visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity gets added to the bill. If the dentist finds n cavities, what will the cost of the visit be? Write your answer as an expression. Alright, so we're talking about the cost of the visit. So you're gonna spend $50 no matter what. And then you're gonna
get an additional charge of $100 per cavity it tells us. An additional charge of $100 per cavity. So lets see, if you have n cavities it's gonna be $100 times n. I can just write this as 100n. Now lets see if this makes sense. If you have no cavities, if n is zero, then you're just gonna pay your $50. But if you have one cavity, you're gonna pay your
$50 plus 100 times one. If you have two cavities, you're gonna pay $50
plus 100 times 2, yeah. This seems to make sense. So lets check our answer. We got it right, lets
do another one of these. Sunny earns $12 per hour delivering cakes. She worked of x hours this week. She worked for X hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week? So if you see that she earns $12 per hour and she worked for x hours. Okay, she got $12 per hour times x hours. So that's how much she would've made except for the fact that she also had, she was charged, I guess her employer, charges her for late delivery. So she had to take $15
out of her paychecks. So this is what she would've gotten paid based on her hourly wage and the number of hours she worked. But then she has that late
fee that she has to pay. So it's gonna be 12 x minus 15 is how much she actually earned this week. Lets do a few more of these. There are c players on
the Cougars hockey team. The team scored a total
of 36 goals this season. One of the players, Matthew,
scored two more goals than the average per player. How many goals did Matthew score? Alright, well lets think
about the average per player. Cause we know that he scored two more than the average player. So the average is going to
be the total number of goals divided by the number of players. And they tell us that they're c players. So this expression right over here, that will tell us the average, that that's the average goals per player. Now we know Matthew scored two more than this thing over here. So we can just add two to that. And that's how many goals Matthew scores. Lets check our answer. Now the key here, this might
seem a little confusing, but remember, this says
Matthew scored two more goals. Two more goals than the average player. The average player, the
average goals per player is 36 divided by c. Lets do one more of these. Hannah has 127 books in her collection. Her school is hosting a book donation. There are z students at her school and they each plan to donate
the same amount of books and reach a total donation of 300 books. How many books will Hannah
have in her collection after her donation? Alright, so lets think about it. Hannah has 127 books in her collection. That's how much she has in her collection. Her school is hosting a book donation. There's z students at her school and they each plan to donate
the same amount of books and reach a total of 300 books. How many books will Hannah
have in her collection after her donation? So 127, and I know I just reread it cause that first time
I was like, okay wait, is 127 the amount of books that Hannah has or the amount that her school
has would be very clear. 127 is the number of book Hannah has. Then she's gonna donate
some of those books. So she's gonna donate some
of those books to her school. And we have to figure out how much is she going to donate to her school. And we see that the
students, the z students plan on together, they each want to donate the same number of books and together they're
gonna donate 300 books. So how much is each
student going to donate? Well, if z students
together are donating 300, each student is going to
donate 300 divided by z. 300 divided by z. And so Hannah starts with 127 books. She's going to donate her
share of books to the school. And each student is going to
donate 300 divided by z books. So Hannah is going to be left with 127 minus 300 over z books after her donation.