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# Moduel 7

### Module 7 - Solving Systems of Linear Equations and Problem Solving

Question | Answer |
---|---|

The sum of two numbers is 76 and their difference is 52. Find the two numbers | X + Y = 76 64 + Y = 76 X - Y = 52 Y = 76 - 64 2X = 128 Y = 12 X=64 |

Three times one number minus a second is 8, and the sum of the numbers is 12. Find the numbers. | 3X - Y = 8 5 + Y = 12 X + Y =12 -5 -5 4X = 20 Y =7 X= 5 |

Last month, Jerry Papa purchased two DVDs and give CDs at wall-to-wall sound for $65. This month, he bought four DVDs and three CDs for $81. Find the price of each DVD and find the price of each CD. | 2X + 5Y = 65 -4X - 10Y = -130 4X + 3Y = 81 4X + 3Y = 81 -7Y = -49 Y= 7 X=15 (Plug Y into equation) |

Sara and Keith Robinson purchased 40 stamps, a mixture of 44cent and 20 cent stamps. Find the number of each type of stamp if they spent $16.40 | .44X + .20Y = 16.40 X+Y= 40 (move decimal so you work with whole numbers) 44X+20Y = 1640 /4 /4 /4 11X+5Y = 410 X+Y= 40 (-.5) 35 + Y=40 -35 -35 Y=5 11X+5Y = 410 -5X-5Y = -200 6X=210 X=35 |

Pratap Puri rowed 18 miles town the Delaware River in 2 hours, but the return trip took 4 1/2 hours. Find the rate Pratap can row in still water and find the rate of the current. Let x = rate Pratap can row in still water and y = rate of current. | Create a chart.d&downriv=18, distance&upriv=18. downriv&r=x+y, downriv&t=2. Upriv&r=x-y, upriv&t=4.5 18=2(x+y)--> 9=x+1 18=4.5(x-y)(4)--> 36=9(x-y) 4x-y x+y=9 x-y=4 2x=13 x=61/2 (plug that in and find that y= 2.5) |

Elise is preparing 15 liters of a 25% saline solution. Elise has two other saline solutions, with strengths of 40&10%. Find the amount of 40% solution and the amount of 10% solution she should mix to get 15 liters of a 25% solution. | x+y=15 x+y=15(-1) -x-y=-15 4x+.1y=.25(.15) 4x+y=37.5 4x+y=37.5 3x=22.5, x=7.5 y=15-7.5, y=7.5 |

According to the MUTCD, a sign must have a perimeter of 60in. Also, its length must be 6 inches longer than its width. Find the dimensions. | p=2l+2w 60=2(w+6)+2w p=60 60=2w+12+2w l=12+6 60 = 4w+12 w=12 l=18 48=4w w=12 |

Find the values of x and y in the isosceles triangle when (3x-10)degrees is an angel outside of the bottom left point. | x+y=180dg x+2y=180dg y+3x-10=180dg x=180-2y y+3(180-2y)-10=180 y+540-6y=190 -5y=190-540 -5y=350 y=70 x=180-70(2)=40 x=40 |

Judy plans to erect 152 feet of fencing around her rectangular horse pasture. A river bank serves as one side length on the rectangle. If each width is 4 ft longer than half the length, find the dimensions. | 2x+y+8+y=152 y+8+y=152 2y=152-8=144 2y=144 y=72 x=y/2+4 x=72/2+4 36+4=40 x=40 |

One number is two more than the second number. Twice the first is 4 less than 3 times the second. Find the numbers | X= Y +2 2X = 3Y - 4 2Y + 4 = 3Y - 4 2Y - 3Y = -4 . 4 - Y = -8 2X- 4 = 3 (-8) 2X - 4 = -24 +4 = -20 2X=-20 X=-10 |

Created by:
nicollettetl