Let's Talk Word Problems

In class today we completed questions 10, 11, 21 and 33. I'd like to walk you through the process of finding the answers to these problems. Please come to class tomorrow prepared with any questions you may have. 

When solving word problems, remember to distinguish between what you know and what you need to know. Remember to pay attention to clues like "more than" and "less than" that will indicated whether you need to add or subtract. 

10. What we know - There are about 778 million km between the sun and Jupiter. 

                                - This is 550 million km greater than the distance between the sun and Mars. 

      What we need to know - The distance (d) between Mars and the sun. 

Let's set up an equation. Ask the question, what's equal to what here? We know that 778 million km is equal to d (the distance between Mars and the sun) plus an extra 550 million km. 

778 = d + 550

Now, solve for d by subtracting 550 from both sides:

778 - 550 = d + 550 - 550

228 = d

The average distance from Mars to the sun is 228 million km. 

11. What we know - Speed travels through steel @ 5200 m/s

                               - This is 2520 m/s faster than the speed of sound through silver

      What we need to know - The speed of sound through silver (s)

What's equal to what here? We know that 5200 m/s is equal to the speed of sound through silver (s) plus an extra 2520 m/s. 

5200 = s + 2520

Now, solve for s by subtracting 2520 from both sides:

5200 - 2520 = s + 2520 - 2520

2680 = s

The speed of sound through silver is 2,680 m/s.

21. What we know - Distance from Venus to the sun is 108 million km.

                               - This distance is 42 million km less than the distance from Earth to the sun/

      What we need to know - Earth's distance (d) from the sun. 

This is very similar to #10. We know that 108 million km is equal to d (the distance between the Earth and the sun) minus 42 million km. 

108 = d - 42

d = 150 

The average distance from the Earth to the sun is 150 million km. 

33. What we know - In '96, 487m people spoke English. 

                               - This was 512m people fewer than the # of people who spoke Mandarin. 

      What we need to know - How many people spoke Mandarin (n)?

We could think of it like this: If 487 million people spoke English, and that was 512 million people less than those who spoke Mandarin, we must subtract 512 from n to get the 487:

n - 512 = 487 (Answer A)

Worksheet Answers 1 - 9

Hola Amigos,
Please check your answers. Click on the pictures to enlarge (answers are boxed). See the comments if your answer was incorrect and you're not sure where you went wrong. Be sure to come prepared to class tomorrow with any questions you have. See you then!

Questions 1-4 were pretty straight forward. Change addition to adding the opposite, distribute (if necessary), and combine like terms. Sometimes it helps to put negative numbers in parentheses so as not to confuse the signs with adding, subtracting, negatives, etc.

Number 5 was a big more complex. After changing subtraction to adding negatives, we distributed both the 3 and the negative 4 to their respective parentheses. Then we used integer rules to combine like terms. Negative 12 and positive 12 cancel each other out.

Number 6 could have been done two ways. The first way would include all the steps we see above. The second would entail looking at the problem and saying, "If I've got six times g minus h, and I'm taking away six times g minus h, I'll be left with zero."

For 7 - 9, don't forget that there's always an imaginary 1 next to any variable that's by itself. Changing a variable to its negative would mean that invisible 1 turns into a negative 1.