02.02 Two-Variable Equations
Essential Questions

·  How can we create equations in two or more variables to represent relationships between quantities?

·  How can we represent constraints by equations or inequalities and interpret solutions as viable or nonviable options in the model?

Main Idea (page #) / DEFINITION OR SUMMARY / EXAMPLE
Two-Variable Equations p.2 / Steps to solving problems / 1.  Read and understand the situation within the word problem.
2.  Identify and pull out ______from the problem.
3.  Assign ______to unknown values.
4.  Set up and solve the equation.
5.  Check that your answer makes sense within the context of the problem.
Consecutive integer problems p.2 / Label the first integer with x, the next with x + 1, the next with x + 2, and so on. / The sum of three consecutive integers is 75.
Set Up: ______
Solution ______
Finding the solution when given the equation p.3 / The problem gives two delivery option equations; the first is for three to five business days and the second is within two business days. Given that Alisha ordered five books, we want to determine how much money she will save if she chooses the longer delivery option. Is it worth it for Alisha to wait a little longer for her books? / C=cost of delivery
X= number of books. In this problem, x=5
Delivery Option 3-5 business days
Total Cost Equation C= 3 + 0.99x, C= 3+.99(5)
Simplify: C=3 + 4.95 so C = 7.95
Delivery Option Within 2 business days
C = 9.99 + 1.99x
Total cost equation C= 9.99 + 1.99x
C= 9.99 + 1.99(5) so C=9.99 + 9.99 so C=______
The cost for five books to be delivered in 3-5 days is $7.95 and the cost for delivery of five books within 2 days is $19.94. What is the difference between the two? Just subtract! The difference between the two delivery options is $19.94 – $7.95, which is $______.
Translating Algebraic Sentences into Equations / The table shows the price of ordering printed photographs of different sizes at an online site. Reyna wants to make a collage with photographs of different sizes. She plans to order the same number of photographs of each size. The equation below represents this situation, where x represents the number of photographs of each size she orders and C represents the total cost of all the photographs.
(0.09)x + (0.79)x + (2.99)x = C
What is the maximum number of photographs she can order in each size for $40?
Once you have your solution, select Check Answer to see if you are correct.
Size / Unit Price
4 x 6 / $0.09
5 x 7 / $0.79
8 x 10 / $2.99
/ The problem gives an equation that relates the cost of ordering photographs, C, and the number of photographs ordered, x. We are given the equation .09 times x plus .79 times x plus 2.99 times x equals C. The problem states that we want to find the maximum number of photographs that Reyna can order in each size for $40. Assign variables to unknown values. X=the number of photographs ordered. C=total cost. Solve: .09 times x plus .79 times x plus 2.99 times x equals C. Replace C with 40. .09 times x plus .79 times x plus 2.99 times x equals 40. Combine like terms. 3.87 times x equals 40. Divide both sides by 3.87
3.87 times x all over 3.87 equals 40 over 3.87x is approx.. equal to 10.3 is approx. equal to 10. Since we are trying to find the number of photographs, we will round our answer down to 10. Check that your answer makes sense within the context of the problem. .09 times x plus .79 times x plus 2.99 times x equals 40. Replace the x with 10 to check the answer. .09 times 10 plus .79 times 10 plus 2.99 times 10 equals 40. .9 plus 7.9 plus 29.9 equals 40. 38.7 equals 40. Since we rounded to 10, we can expect our solution to be a little below 40, which it is. Therefore, we can be confident in our solution as we rounded. Therefore, Reyna can order 10 photos in each size for $40 with our answer rounded to the nearest whole number.