Using Numerical and Algebraic Expressions and

Equations

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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

chickensandwiches

chickentenders

total meals

c + 2c = 225 3c = 225 3 3 c = 75

The cafeteria sold 150 grilled chicken sandwiches and 75 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 = 92m + 7 = -7 -7 2m = 2 2 2 m = 1Julie needs 1 inches on each side.

14

12

12

14

9

both sides of the mat

size ofpicture

size of frame

12

12

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.

30g

cost ofone videogame

number of games

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

cost ofone videogame

number of games

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 ofone videogame

numberof games

the total amount

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?

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?Define your variable.

12

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? Define the variable.

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 = 239B 9d + 68 = 239C 68d + 9 = 239D 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? Define the variable.

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.

Define the variable then 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?

Define the variable then write and solve an equation to determine the number of packs of pens Rachel can buy.

Be prepared to show your equation!

113 The length of a rectangle is 9 cm greater than its width and its perimeter is 82 cm.

Define the variable then write and solve an equation to determine the width of the rectangle.

Be prepared to show your equation!

114 The product of -4 and the sum of 7 more than a number is -96.

Define the variable then write and solve an equation to determine the number. Be prepared to show your equation!

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.

Define the variable then 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?

116 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.

Define the variable then 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?

117 The perimeter of a hexagon is 13.2 cm.

Define the variable then write and solve an equation to determine the length of a side of the hexagon.

Be prepared to show your equation!