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Evaluating expressions with variables word problems

Learn to evaluate expressions in word problems to gain new information. 
Khan Academy video wrapper
Evaluating an expression with one variableSee video transcript

Reflection question

What was Sal finding when he plugged t=10 into the expression 5t+3?
Choose 1 answer:

Let's try a practice problem!

The expression 2m+10c gives the amount of money, in dollars, a dessert store makes from selling m muffins and c cakes.
How much money does the dessert store make from selling three muffins and four cakes?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dollars

Challenge problem

Part A
A flower store uses the expression 2+5r to determine the cost, in dollars, of r roses.
Complete the table to find the cost of different numbers of roses.
Number of roses (r)Cost (2+5r)
317
6
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
9
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Part B
Cam has 32 dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Extra challenge

Explain to a family member, friend, or classmate why the cost of six roses is not double the cost of three roses.

Want to join the conversation?

  • starky tree style avatar for user TrySmarter101
    This extra challenge has frozen the two brain cells I had to rub together, and fried them at the same time, which I did not know was possible. There's simply not enough information to make an informed, rational decision. I mean, who's writing these challenges? 10 out of 10 for style... I think it has something to do with overhead costs and distance to travel, but I just can't sort it out with any clarity.
    (63 votes)
    Default Khan Academy avatar avatar for user
    • primosaur seed style avatar for user Ian Pulizzotto
      The expression 2 + 5r for the total cost of r roses means $5 per rose plus a constant $2 fee for the entire purchase. If the number of roses is doubled (for example, 6 roses instead of 3 roses), only the cost of the roses without the fee is doubled, but the $2 fee is not doubled to $4. So doubling the number of roses comes $2 short of doubling the total cost.

      Algebraically, the total cost of 2r roses is 2 + 5(2r) = 2 + 10r dollars.
      However, twice the total cost of r roses would be 2(2 + 5r) = 2(2) + 2(5r) = 4 + 10r dollars.
      So once again, we see that doubling the number of roses comes $2 short of doubling the total cost.

      Have a blessed, wonderful day!
      (70 votes)
  • leaf blue style avatar for user Madelyn Paton
    how do you find the value of the muffins and cakes? it doesn't give enough info?
    (14 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Denis Orlov
      It gives all the info you need.
      We have the expression:
      2m+10c
      Where m are muffins and c are cakes.

      the question is : How much money does the dessert store make from selling three muffins and four cakes?

      So m = 3 and c = 4
      Now just plug muffins and cakes into the expression 2m+10c
      2(3) + 10(4) or 2*3+10*4, both are the same thing

      Now do the multiplication first and it becomes:
      6 + 40
      = 46

      $46 dollars for 3 muffins and 4 cakes
      (26 votes)
  • blobby green style avatar for user gmmkyingtao
    the extra challenge is making me loose my brain cells
    (17 votes)
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  • piceratops tree style avatar for user Subnauticaplayer88
    What does it mean mathematically if you "plug something in"?
    (6 votes)
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  • leafers sapling style avatar for user Daniel Ungureanu
    Cam has 32 dollars. How many roses can he afford to buy?
    Assume that he wants to buy as many roses as he can. The answer is he can buy 6 roses for $32 but I do not understand why that is the answer.
    (5 votes)
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  • aqualine tree style avatar for user Angeleen23
    I literally don't understand anything why is the first answer 10 and not 53 that makes no sense if I were to multiply 5 by ten that would be 50 and if I add 3 that would be 53 this makes no sense what so ever
    (5 votes)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      1st Question: What is Sal finding when he uses t=10?
      The problem tells you "t" is the number of tickets. And, it tells you that the expression calculates the cost of tickets. So, if Sal is using t=10, he is find the cost of 10 tickets. The question didn't ask you to find the cost. It asked you what the end result would represent.

      Also, the last option (the number of tickets that you can buy for $53) assumes that you know the cost and you don't know the number of tickets. The tickets is the given value.

      Hope this helps.
      (10 votes)
  • mr pants purple style avatar for user Nathaniel Lawrence
    can you explain 100+20(51/4)
    (6 votes)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      100+20(5 1/4)
      Follow order of operations rules - PEMDAS:
      You must multiply 1st.
      -- Change 5 1/4 into an improper fraction = 21/4
      -- Multiply: 20 (21/4) = 20/1 * 21/4 = 5 (21) = 105

      Your expression is now: 100+105
      Add the 2 numbers and you'll have your answer.
      (7 votes)
  • blobby green style avatar for user tulipmitchell
    I have no idea how to do this. Can someone explain what he did in the video?
    (6 votes)
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  • blobby green style avatar for user akawessa63
    I do not understand the second one the problem
    (6 votes)
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  • leaf green style avatar for user Daphne
    I can't explain the extra challenge. I just used the formula that they said to use.
    (4 votes)
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    • aqualine ultimate style avatar for user Poonam.Renu
      The explanation is that the cost of 6 roses is not the same as the double the cost of 3 roses because after you multiply 6 by 5 you also have to add an extra 2 because that will make it 7r. After adding the cot will change no matter what. So if they had only told us 5r and do not add 2 then it would be the double of 3, but they also said to add 2 which makes this different from 3.

      Hope this helps :)
      (1 vote)