My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree4Thanks
  • 1 Post By weirddave
  • 2 Post By skeeter
  • 1 Post By weirddave
Reply
 
LinkBack Thread Tools Display Modes
March 30th, 2017, 03:45 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?
baldgeezer is offline  
 
March 30th, 2017, 04:31 AM   #2
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 765
Thanks: 288

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
Thanks from v8archie
weirddave is offline  
March 30th, 2017, 04:52 AM   #3
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,782
Thanks: 2197

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*}
v8archie is offline  
March 30th, 2017, 04:52 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.
baldgeezer is offline  
March 30th, 2017, 05:05 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?
baldgeezer is offline  
March 30th, 2017, 05:55 AM   #6
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,550
Thanks: 1260

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?
Thanks from greg1313 and Posher
skeeter is online now  
March 30th, 2017, 06:18 AM   #7
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 765
Thanks: 288

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
Thanks from baldgeezer
weirddave is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
block, equation, mind



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
hello all :) I don't know where I can put algorithms and please don't block this )) Schoff43 Algebra 2 November 22nd, 2014 12:45 AM
What is a block matrix? mick7 Linear Algebra 0 March 9th, 2014 09:38 AM
The sum of diagonal block matrix nbdxkfq Linear Algebra 0 August 23rd, 2013 07:53 PM
A 2.00 kg block r-soy Physics 4 December 25th, 2010 06:52 AM
block matrix determinant guroten Linear Algebra 0 November 23rd, 2009 11:29 AM





Copyright © 2017 My Math Forum. All rights reserved.