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March 30th, 2017, 04:06 AM  #1 
Newbie Joined: Mar 2017 From: UK Posts: 5 Thanks: 0  Simultaneous Equations  Help please
My daughter needs help with the following questions. Can anyone provide the right formulas and workings please so I can help her through the questions. I have a number of bunnies and a number of chicks. Altogether, they have 22 legs and 16 eyes. Use simultaneous equations to find out how many chicks I have and how many bunnies I have. 5 chicks have a mean mass of 65g. The same 5 chicks put together with 4 bunnies have a mean mass of 525g. What is the mean mass of the 4 bunnies? Each year, the size of a population of bunnies increases by 13% of the previous year’s population size. If the population is 45 in April 2017, what will its size be in April 2027? The height of a chick is 15cm less than the height of a bunny. The height of 8 chicks and 5 bunnies is 1.92m. Use algebra to find out the height of each in cm. A bunny runs 70cm along the ramp to its hutch. The ramp is positioned at an angle of 22° to the horizontal. How high is the hutch from the floor? When a bunny and a chick have a race, the probability that the bunny wins is 0.9. When a bunny and a chick have a jumping competition, the probability that the chick wins is 0.3. If a bunny and a chick have a race and then a jumping competition, what is the probability that they will each win exactly one of the competitions? 
March 30th, 2017, 08:44 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,683 Thanks: 1522 
Assign variables for the unknowns, especially what you are asked to find. Suppose I have b bunnies, each with 2 eyes and 4 legs, and c chicks, each with 2 eyes with 2 legs. 4b + 2c = 22 2b + 2c = 16 By subtraction, 2b = 6, so b = 3. By substitution, 6 + 2c = 16, so c = 5. I have 3 bunnies and 5 chicks. The question about the 70cm ramp requires use of trigonometry. To get the answer, multiply 70cm by sin(22°). 
April 18th, 2017, 02:43 PM  #3 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68 
The total mass of all the creatures is 9×525g, that is, 4725g. The total mass of the chicks is 5×65, that is, 325g. So the total mass of the bunnies is (4725g325g), that is, 4400g. ∴ The mean mass of the bunnies is (4400g÷4), that is, 1100g. 
April 19th, 2017, 08:31 AM  #4 
Banned Camp Joined: Apr 2017 From: durban Posts: 22 Thanks: 0 Math Focus: Algebra 
There is another way out 5c + 4b=525 C+c+c+c+c+b+b+b+b/9=525 5c + 4b =525x9 5c+4b=4725 Where c=65g 5(65)+4b=4725 325+4b=4725 4b=4725325 4b=4400 B=4400/4 B=1100g 
April 19th, 2017, 08:45 AM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,686 Thanks: 666 Math Focus: Wibbly wobbly timeywimey stuff.  

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