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March 30th, 2017, 04:06 AM   #1
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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?
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March 30th, 2017, 08:44 AM   #2
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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°).
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April 18th, 2017, 02:43 PM   #3
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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 (4725g-325g), that is, 4400g.
∴ The mean mass of the bunnies is (4400g÷4), that is, 1100g.
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April 19th, 2017, 08:31 AM   #4
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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=4725-325
4b=4400
B=4400/4
B=1100g
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April 19th, 2017, 08:45 AM   #5
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Quote:
Originally Posted by Ola Lawson View Post
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=4725-325
4b=4400
B=4400/4
B=1100g
Quick fix, though the step isn't required. You can go from step 1 to step 3 immediately.

-Dan
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