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Using Numerical and Algebraic Expressions and Equations DAY 8. Return to table of contents. We can use our algebraic translating skills to solve other problems. We can use a variable to show an unknown. A constant will be any fixed amount.
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Using Numerical and Algebraic Expressions and Equations DAY 8 Return to table of contents
We can use our algebraic translating skills to solve other problems. We can use a variable to show an unknown. A constant will be any fixed amount. If there are two separate unknowns, relate one to the other.
The school cafeteria sold 225 chicken meals today. They sold twice the number of grilled chicken sandwiches than chicken tenders. How many of each were sold? 2c + c = 225 c + 2c = 225 3c = 225 3 3 c = 75 The cafeteria sold 150 grilled chicken sandwiches and 75 tenders. chicken sandwiches total meals chicken tenders
Julie is matting a picture in a frame. Her frame is 9 inches wide and her picture is 7 inches wide. How much matting should she put on either side? 2m + 7 = 1 2 1 2 2m + 7 = -7 -7 2m = 2 2 2 m = 1 Julie needs 1 inches on each side. 9 9 1 2 1 2 both sides of the mat size of picture size of frame 1 4 1 4
Many times with equations there will be one number that will be the same no matter what (constant) and one that can be changed based on the problem (variable and coefficient). Example: George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?
George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all? Notice that the video games are "per game" so that means there could be many different amounts of games and therefore many different prices. This is shown by writing the amount for one game next to a variable to indicate any number of games. cost of one video game number of games 30g
George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all? Notice also that there is a specific amount that is charged no matter what, the flat fee. This will not change so it is the constant and it will be added (or subtracted) from the other part of the problem. 30g + 7 number of games cost of one video game the cost of the shipping
George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all? "Total" means equal so here is how to write the rest of the equation. 30g + 7 = 127 cost of one video game the cost of the shipping number of games the total amount
George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all? Now we can solve it. 30g + 7 = 127 -7 -7 30g= 120 30 30 g = 4 George bought 4 video games.
106 Lorena has a garden and wants to put a gate to her fence directly in the middle of one side. The whole length of the fence is 24 feet. If the gate is 4 feet, how many feet should be on either side of the fence? 1 2
107 Lewis wants to go to the amusement park with his family. The cost is $12.00 for parking plus $27.00 per person to enter the park. Lewis and his family spent $147. Which equation shows this problem? A 12p + 27 = 147 B 12p + 27p = 147 C 27p + 12 = 147 D 39p = 147
108 Lewis wants to go to the amusement park with his family. The cost is $12.00 for parking plus $27.00 per person to enter the park. Lewis and his family spent $147. How many people went to the amusement park WITH Lewis?
109 Mary is saving up for a new bicycle that is $239. She has $68.00 already saved. If she wants to put away $9.00 per week, how many weeks will it take to save enough for her bicycle? Which equation represents the situation? A 9 + 68 = 239 B 9d + 68 = 239 C 68d + 9 = 239 D 77d = 239
110 Mary is saving up for a new bicycle that is $239. She has $68.00 already saved. If she wants to put away $9.00 per week, how many weeks will it take to save enough for her bicycle?
111 You are selling t-shirts for $15 each as a fundraiser. You sold 17 less today then you did yesterday. Altogether you have raised $675. Write and solve an equation to determine the number of t-shirts you sold today. Be prepared to show your equation!
112 Rachel bought $12.53 worth of school supplies. She still needs to buy pens which are $2.49 per pack. She has a total of $20.00 to spend on school supplies. How many packs of pens can she buy? Write and solve an equation to determine the number of packs of pens Rachel can buy. Be prepared to show your equation!
The length of a rectangle is 9 cm greater than its width and its perimeter is 82 cm. Write and solve an equation to determine the width of the rectangle. Be prepared to show your equation! 113
The product of -4 and the sum of 7 more than a number is -96. Write and solve an equation to determine the number. Be prepared to show your equation! 114
A magazine company has 2,100 more subscribers this year than last year. Their magazine sells for $182 per year. Their combined income from last year and this year is $2,566,200. Write and solve an equation to determine the number of subscribers they had each year. Be prepared to show your equation! How many subscribers last year? 115
A magazine company has 2,100 more subscribers this year than last year. Their magazine sells for $182 per year. Their combined income from last year and this year is $2,566,200. Write and solve an equation to determine the number of subscribers they had each year. Be prepared to show your equation! How many subscribers this year? 116
117 The perimeter of a hexagon is 13.2 cm. Write and solve an equation to determine the length of a side of the hexagon. Be prepared to show your equation!
