
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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March 30th, 2017, 04:45 AM  #1 
Newbie Joined: Mar 2017 From: UK Posts: 5 Thanks: 0  Equation Mind Block
Hi, I was helping my child with maths homework and while doing some simultaneous equations we came up against this problem. I couldn't for the life of me work out how to write and solve the following equation  instead, I worked it out in my head. Can someone show me the correct method so I can pass it on please. Luca has some 10 pence pieces and some five pence pieces. Altogether, he has 40 coins which total £3.15. How many of each coin does he have? 
March 30th, 2017, 05:31 AM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 786 Thanks: 294 
let 'x' be the number of 10p and 'y' be the number of 5p We have enough information to write the following 2 equations: 1) 10x + 5y = 315 2) x + y = 40 rearranging (2) we get: x = 40  y which we can substitute into (1) to get: 10(40  y) +5y = 315 400  10y + 5y = 315 5y = 85 y = 17 we can now substitute that into (1) to get: x + 17 = 40 x = 23 So, we have 23 10p and 17 5p 
March 30th, 2017, 05:52 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,091 Thanks: 2360 Math Focus: Mainly analysis and algebra 
An alternative way to solve the simultaneous equations: \begin{align*} 10x + 5y &= 315 \\ x + y &= 40 \implies 5x + 5y = 200 \\ (10x + 5y)  (5x + 5y) &= 315  200 \\ 5x &= 115 \implies \boxed{x = 23} \\ y &= 40  x \implies \boxed{y = 17} \end{align*} 
March 30th, 2017, 05:52 AM  #4 
Newbie Joined: Mar 2017 From: UK Posts: 5 Thanks: 0 
So simple when you see it written in front of you. Thanks so much for the help.

March 30th, 2017, 06:05 AM  #5 
Newbie Joined: Mar 2017 From: UK Posts: 5 Thanks: 0 
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? 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, 06:55 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339 
Your (or I should say your "child's") problem involving simultaneous equations has been solved by the methods of substitution and elimination. The first problem on the laundry list of bunny/chick problems involves the same concept. Why don't you have him/her try solving the legs/eyes problems on his/her own and post up the attempt? 
March 30th, 2017, 07:18 AM  #7 
Senior Member Joined: Apr 2014 From: UK Posts: 786 Thanks: 294 
Assuming the normal number of legs and eyes for each animal and using b for the number of bunnies and c for chicks: 1) 2b +2c = 16 eyes, therefore b + c = 8 (animals) 2) 4b + 2c = 22 legs, 2b + c = 11 (sets of 2 legs) using (1), c = 8  b into (2): 2b + (8  b) = 11 b = 3 (bunnies!) back into (1) 3 + c = 8 c = 5 (chicks!) The mass of all the chicks is 5 * 65, the mass of all the animals is 9 * 525, so the mass of the 4 bunnies is 9*525  5*65 = 4400, which is a mean bunny mass of 1100g. Adding gravy will help bring the weight back up after cooking. Assuming "70CM along" means the hypotenuse, then it's erm, ~26CM. I can't do probability 

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