More on Solving Equations

Grouping Symbols on Both Sides…… You might have to distribute before you combine like terms.

Solve: 2(x+5)= 3(x + 2) + x Answer: 2x + 10 = 3(x + 2) + x __________________ -2x + 10 = 6 -10 -10 -2x = -4 x = 2 2(x+5)= 3(x + 2) + x

Solve: 2(3x + 2) = 2(x+8) Answer: 2(3x + 2) = 2x + 16 6x + 4 = 2x + 16 ________________ 4x + 4 = 16 -4 -4 _________________ 4x = 12 x = 3 2(3x + 2) = 2(x+8)

Word Problems

Words that tell you to add…. Plus Increased By Sum More Than

Words that tell you to subtract… Minus Decreased By Difference Less Than

Multiply and Divide Words…..

Write the mathematical statement for the following….. 9 increased by 2 5 decreased by m Sum of 4 and 2x 7 less than 12 7 increased by 5 times a number 8 decreased by 3 times a number The sum of twice a number and 5 9 + 2 5 – m 4 + 2x 12 – 7 7 + 5n 8 – 3x 2y + 5

You Try….. The sum of 7 and 3 times a number 4 times Harry’s age increased by 2 8 pounds less than twice wanda’s weight 7 + 3n 4h + 2 2w - 8

Word Problems…… The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit Let’s define the variables first: Let C = Cost Let P = Profit Let SP = Selling Price

The $500 selling price of a TV is $70 less than 3 times the cost The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit. Think: Cost + Profit = Selling Price C + P = SP We know the selling price and are looking for the profit. Somehow we need to find the cost first: 3C – 70 = $500 3C = $570 Cost = $190. We are still looking for the profit.

Cost + Profit = Selling Price. 190 + P = 500 P = 500 – 190 The $500 selling price of a TV is $70 less than 3 times the cost. Find the profit. We know that the cost = 190. Cost + Profit = Selling Price. 190 + P = 500 P = 500 – 190 Profit = $310 (This is the answer)

You Try…… The $140 selling price of a game is $60 less than twice the cost. Find the profit.

The $140 selling price of a game is $60 less than twice the cost The $140 selling price of a game is $60 less than twice the cost. Find the profit. 1st find the cost: 2C – 60 = 140 2C = 140 + 60 2C = 200 C = $100 2nd find the profit: C + P = SP 100 + P = 140 P = 140 – 100 Profit = $40

Example…… Mr. Daniel’s family rented a car when they flew to Hawaii for a 3-day vacation. They paid $42 per day and $0.07 for each mile driven. How much did it cost to rent the car for 3 days and drive 200 miles?

Answer….. Mr. Daniel’s family rented a car when they flew to Hawaii for a 3-day vacation. They paid $42 per day and $0.07 for each mile driven. How much did it cost to rent the car for 3 days and drive 200 miles? Total Cost = (Cost Per Day)(# of Days) + (Cost Per Mile)(# of Miles) Cost = (42)(3) + (200)(0.07) Cost = $126 + $14 Cost = $140

Answer…… A car repair shop charged Mr. Jacobs $96 for an automotive part plus $72 per hour that a mechanic worked to install the part. The total charge was $388. For about how long did the mechanic work to install the part on Mr. Jacob’s car? Total Cost = Base fee + (Charge Per Hour)(# of hours) $388 = $96 + $72(hours) 388 = 96 + 72H 388 – 96 = 72H 292 = 72H H = 4.06 or 4 Hours

Example…… A car repair shop charged Mr. Jacobs $96 for an automotive part plus $72 per hour that a mechanic worked to install the part. The total charge was $388. For about how long did the mechanic work to install the part on Mr. Jacob’s car?

Example…… The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle.

Answer…… The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle. 1st: Find the width by using the area formula of a rectangle. A = length x width 35 = 5 x width width = 7

Remember the width = 7…. The length of a rectangle is 5 and the area is 35. Find the perimeter of the rectangle. 2nd: Plug into the formula to find the perimeter. P = 2l + 2w P = 2(5) + 2(7) P = 10 + 14 P = 24

Example…… The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle.

Answer….. The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle. 1st: Find the length using the perimeter formula. P = 2w + 2l 20 = 2(4) + 2l 20 = 8 + 2l 12 = 2l l = 6

Remember the length = 6….. The perimeter of a rectangle is 20 and the width is 4. Find the area of the rectangle. 2nd: Find the area. A = l x w A = 6 x 4 A = 24