|March 30th, 2017, 04:06 AM||#1|
Joined: Mar 2017
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|
Joined: Dec 2006
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|
Joined: Jan 2014
From: The backwoods of Northern Ontario
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.
|April 19th, 2017, 08:31 AM||#4|
Joined: Apr 2017
Math Focus: Algebra
There is another way out
5c + 4b=525
5c + 4b =525x9
|April 19th, 2017, 08:45 AM||#5|
Joined: May 2013
From: The Astral plane
Math Focus: Wibbly wobbly timey-wimey stuff.
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