CCGPS Assignment 1
Linear Word Problems Name_______________________________________
|Cara’s Candles #1 -7 |Mrs. Howell #8 -11 |
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|MCC9-12.A.CED.3, MCC9-12.N.Q.1-3 |MCC9-12.A.CED.2 Create eqns/inequalities in TWO variables |
|Cara’s taller candle is 16 cm tall. It loses 2.5 cm in height each hour it | |
|burns. Her short candle is 12 cm tall and loses 1.5 cm in height for each |Mrs. Howell, your science teacher, told you that there was a formula to convert |
|hour that it burns. Cara wants to know if these two candles would ever |Celsius into Fahrenheit. She wants you to “discover” this formula for yourself. |
|reach the same height if she lit them at the same time. |The freezing point of water is 0(C and 32(F |
| |The boiling point of water is 100(C and 212(F |
|1.) Finish the table for Cara. | |
|Time (hrs) |8.) Find the equation of the line that goes through the points (0, 32) and (100, |
|0 |212). |
|1 | |
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|6 | |
|7 | |
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|16cm | |
|16 |9.) What’s the formula for changing Celsius into Fahrenheit? |
|13.5 | |
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| |MCC9-12.A.CED.3 Represent Constraints graphically |
| |10.) Graph your line segment. Which is your independent variable(C or F)? |
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| |[pic] |
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|12cm |MCC9-12.A.CED.4 Rearrange Formulas |
|12 |11.) What’s the formula for changing Fahrenheit into Celsius? |
|10.5 | |
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|2.) Use the data in the table to determine what time the two candles will be| |
|at the same height. | |
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|3.) At what height are the two candles the same? Write a complete sentence| |
|and incorporate your answer from #7. | |
|[pic] | |
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|5.) In y = mx + b, | |
|what represents rate of change? | |
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|what represents the initial height of the candles? | |
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|6.) What are the equations of the two lines whose points you plotted? | |
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|7.) How else could you figure out when the candles were at the same height?| |
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|Unknonw numbers #12 -35 |20.) Find four consecutive even integers whose sum is 244. |
|Write an equation (2 pts) and solve it (2 pts) | |
|MCC9-12.A.CED.1 Create eqns in ONE variable | |
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|12.) Matching: | |
|A number less than 2 a.) x – 2 |21.) A rectangle is 12m longer than it is wide. Its perimeter is 68m. Find its |
|A number is less than 2 b.) 2 – x |length and width. |
|The width is 2cm shorter c.) x < 2 | |
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|13.) The sum of 38 and twice a number is 124. Find the number. | |
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| |22.) The length of a rectangle is 4 cm more than the width and the perimeter is at |
|14.) Four less than twice a number is equal to three times the difference of|least 48 cm. What are the smallest possible dimensions for the rectangle? |
|that number and 5. Find the number. | |
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| |23.) Find three consecutive integers whose sum is 171. |
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|15.) Use , ( for each of the following. | |
|Fewer than | |
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|More than | |
|At most |24.) Alex has twice as much money as Jennifer. Jennifer has $6 less than |
| |Charlie. All together, they have $54. How much money does each have? |
|At least | |
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|Less than | |
|No less than | |
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|16.) Consecutive integers are numbers that occur one after another. For | |
|example, 11 and 12 are consecutive numbers. | |
| |25.) There are three exams in a marking period. A student received grades of 75 |
|If 11 = x, then 12 = ________ |and 81 on the first two exams. What grade must the student earn on the last exam to |
| |get an average of no less than 80 for the marking period? |
|17.) Consecutive odd numbers are odd numbers that occur one after another. | |
|For example, 11 and 13 are consecutive odd numbers. | |
|If 11 = x, then 13 = ________ | |
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|18.) The sum of two consecutive integers is less than 83. Find the pair of | |
|integers with the greatest sum. | |
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|19.) The sum of two consecutive numbers is 37. Find the numbers. | |
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Linear Word Problems Homework 1 Name_______________________________________
|1.) In y = mx + b, |The Penny Pattern |
|what represents rate of change? |Stage 1: |
| |Stage one of the pattern is shown — one penny surrounded by six additional pennies.|
|what represents the initial amount @ t = 0 ? |To create each additional stage of the design, place more pennies extending out from|
| |the six that surround the center penny. |
|2.) Margie’s initial weight is 250lbs and loses 5lbs/mon. | |
|Greg’s initial weight was 300lbs and loses 10 lbs/mon. |Stage 2: Stage 3: |
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|Fill in the table with their weight with respect to months |[pic] |
|Time (mon) | |
|2 | |
|4 |6.) Using your penny pattern or the sketches of your penny pattern, create a table|
|6 |of values. |
|8 |Stage |
|10 |1 |
|12 |2 |
|14 |3 |
|16 |4 |
| |5 |
|Marg | |
| |Pennies of Required |
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| |7.) How many pennies are needed to make stage 6? |
|Greg | |
| |How many pennies are needed to make stage 7? |
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| |How many pennies are needed to make stage 8? |
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| |8.) Write an algebraic model that expresses the relationship between the stage |
| |number, n, and the number of pennies required to make that design, p. |
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|3.) Graph the points from the table | |
|[pic] | |
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|4.) What does the point of intersection represent? Write in complete sentences | |
|expressing your full detailed thoughts. | |
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| |9.) Use your model to determine how many pennies are needed to make stage 80, stage|
| |95, and stage 100 of the penny pattern. |
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|5.) An animals runs at a constant speed down a road that has clearly marked mile | |
|markers, but we don’t know where he was @ t = 0. At t = 1hr, he was at the 17th | |
|mile marker, and at t = 3hrs, he was at the 32nd mile marker. Write an equation | |
|that gives us his position based on any time, t. | |
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Linear Word Problems Homework 2 Name_______________________________________
|1.) The sum of three consecutive integers is -114. Find the integers. |7.) The length of a rectangle exceeds its width by 8 inches. The perimeter is 80 |
| |inches. Find the length and width. |
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|2.) The sum of four consecutive integers is -294. Find the integers. |8.) The lengths of the sides of a triangle are represented by three consecutive |
| |even integers. If the perimeter of the triangle is 96 feet, find the lengths of the|
| |sides. |
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|3.) The sum of three consecutive integers is 71 less than the least of the | |
|integers. Find the integers. |9.) The perimeter of a triangle is 40 inches. The second side exceeds twice the |
| |first side by 1 inch, and the third side is 2 inches less than the second side. |
| |Find the length of each side of the triangle. |
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|4.) The sum of three consecutive even integers is -360. Find the integers. |10.) Separate 197 into two parts so that one part is three less than four times as |
| |much as the other part. Find each part. |
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|5.) The sum of three consecutive odd integers is -75. Find the integers. |11.) A student received grades of 92, 95, and 81 on the first three exams. What |
| |grade must the student earn on the fourth exam to get an average of no less than an |
| |A? |
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|6.) The sum of four consecutive even integers equals seven times the greatest of | |
|the integers. Find the integers. |12.) A student received grades of 60, 75, 67, and 62 on the first four exams. What|
| |grade must the student earn on the fifth exam to pass the class? |
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Extra Homework can be found at:
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4.) Graph the lines (by plotting the points) for the 16cm candle and the 12cm candle. Label each line.
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