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# Module 7

### Solving Systems of Linear Equations and Problem Solving

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

Use the addition method to solve the system {X+Y = 83 {X-Y = 17 | X+X=83 X-Y=17 2X = 100 Isolate X 2X/2 = 100/2 X = 50 Use 50 in place of X 50 + Y = 83 Subtract 50 from both sides -50 = -50 Y = 33 |

Ann has been pricing train fares for group rates. One group consists of 3 adults and 4 children which costs $159. The other group consists of 2 adults and 3 children which costs $112. What are the prices of the Adult tickets and the child tickets. | a = price of adult c = price of child group 1 {3a + 4c = $159 group 2 {2a + 3c = $112 { 9a + 12c = 477 {-8a - 12c = -448 a = 29 3(29)+4c = 159 87 +4c = 159 -87 -87 4c = 72 4c/4 = 72/4 c=18 |

A trail is 1200 miles and it goes through 4 towns. A group of hikers start at each town and walk toward each other. They meet after a time of 240 hours. If one group travels 1/2 mile per hour slower then the other group, find the rate of each group. | r . t = d one group is X, one group is Y 240x + 240y = 1200 x + 1/2 = y 240x 240(x + 1/2) = 1200 240x + 240x + 120 = 1200 480x + 120 = 1200 - 120 = -120 480x = 1080 480x/480 = 1080/480 x = 2 1/4 mph 2 1/4 + 1/2 = y 2 3/4 = y |

A chemist needs to prepare 12 liters of a 9% solution. Find the amount of a 4% solution and the amount of a 12% solution that she should mix to get the solution. | group 1 {X + Y = 12 group 2 {0.04X + 0.12Y = 0.09(12) -4X - 4Y = -48 4X + 12Y = 108 8Y = 60 8Y/8 = 60/8 Y = 7 1/2 Liters 4X + 12(7 1/2) = 108 4X + 90 = 108 -90 = -90 4X = 18 4X/4 = 18/4 X=4 1/2 Liters |

Recall two angels are complimentary if the sum of their measures is 90 degrees. Find the measures of two complimentary angels if one angel is twice the other. | group 1 {X + Y = 90 group 2 {Y = 2X Use Y value of 2X in group 1 X + 2X = 90 3X = 90 3X/3 = 90/3 X = 30 degrees Use X value of 30 in group 2 Y = 2(30) Y = 60 degrees |

New computer desks for a company estimate total cost of new desks to be $6000. The cost of each desk is $200. The revenue from each desk will be $450. | R(X) = 450X C(X) = 6000 + 200X 450X = 6000 + 200X -200X = - 200X 250X = 6000 250X/250 = 6000/250 X = 24 computer desks to break even Revenue = 450(24) = $10800 Cost = 6000 + 200(24) 6000 + 4800 = $10800 |

The measure of the largest angle of a triangle is 80 degrees more than the measure of the smallest angle, and the measure of the remaining angle is 10 degrees more than the measure of the smallest angle. Find the measure of each angle. | Sum of the degree of a triangle is 180 degrees {Y = X + 80 {Z = X + 10 {X + Y + Z = 180 X + (X + 80) + (X + 10) = 180 3X + 90 = 180 -90 = -90 3X = 90 3X/3 = 90/3 X = 30 Y = 30+80=110 Y = 110 Z = 30 + 10 Z = 40 (30,110,40) |

Created by:
greenejoy