# Write an equation to solve these problems

• Jun 1st 2009, 07:17 AM
Beginner101
Write an equation to solve these problems
Hi

I have exams in a few weeks and am stuck on some basic questions which the teacher hasn't taught due to their 3 month absence. We didn't finish the syllabus so now I have no notes on this and have no idea (Crying)

I have searched the internet and tried for 2 days, even through some revision guides but I just can't work it out. The answers to some are very easy but the equations I'm perplexed at. I learn through examples and then questioning, not through other methods. If someone can help me with one example, with some general pointers and principles, I'll then try and apply the same principles to the rest to work them out. (this is a mock exam I'm practising at home)

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Equations and Inequalities

1. Write down an equation and use it to solve the following problems.
(me: I don't even get if its asking for one equation to solve all the problems or one equation per problem?)

a) Demelza's dad is three time as old as Demelza. The sum of their ages is 52. How old is Demelza?

me: 1/4 x 52 = 13. Demelza is 13 and the dad is 3x13 = 39. 39+13 = 52. Took me about 10s to work out. But I don't even know where to start to put this into an equation.

b) Three consecutive odd numbers add up to 93. Find these numbers.

me: 29+31+33 = 93. Took me less than 7s to work out. I'm clueless about putting it into an equation.

c) Jack and Jill went up the hill to fetch a pail of water. The water weighed 15KG more than the pail. The total weight was 18KG. How heavy was the pail?

me: 18-15 = 3. Pail was 3KG. Is that it? That took less than a second. That seems a bit too simple...

d) Tweedledum and Tweedledee bought a cake and cut it into 3 pieces, one piece for each of them and one piece for Alice. Tweedledum's piece was 50g heavier than Tweedledee's piece. Tweedledee's piece was 30g heavier than Alice's piece. The total mass was 710g. What was the mass of Alice's piece?

me: That took 2 days. I don't know how to start with this honestly like what method to use. I'm missing a systematic approach to all these.

Thank you
• Jun 1st 2009, 07:54 AM
masters
Quote:

Originally Posted by Beginner101

---------------

Equations and Inequalities

1. Write down an equation and use it to solve the following problems.
(me: I don't even get if its asking for one equation to solve all the problems or one equation per problem?)

Hi beginner101,

The key to untangling word problems is to “divide and conquer”. Break the problem down into smaller bits, state each bit, establish an equation or equations and solve.

a) Demelza's dad is three time as old as Demelza. The sum of their ages is 52. How old is Demelza?

Let x = Demelza's age.

Let 3x = Demelza's dad's age

Let 52 = the sum of their ages

Equation: x + 3x = 52

me: 1/4 x 52 = 13. Demelza is 13 and the dad is 3x13 = 39. 39+13 = 52. Took me about 10s to work out. But I don't even know where to start to put this into an equation.

Solve the above equation this way.

x + 3x = 52
Combine terms

4x = 52
Divide by 4

x = 13 (Demelza's age)

3x = 3(13) = 39 (Demelza's dad's age)

Quote:

b) Three consecutive odd numbers add up to 93. Find these numbers.

me: 29+31+33 = 93. Took me less than 7s to work out. I'm clueless about putting it into an equation.
Let x = the first odd integer

Let x + 2 = the 2nd odd integer

Let x + 4 = the 3rd odd integer

Let 93 = the sum of the 3 odd integers

Equation: x + x + 2 + x + 4 = 93

Combine terms and solve as before.

Quote:

c) Jack and Jill went up the hill to fetch a pail of water. The water weighed 15KG more than the pail. The total weight was 18KG. How heavy was the pail?

me: 18-15 = 3. Pail was 3KG. Is that it? That took less than a second. That seems a bit too simple...
Let x = weight of the pail

Let x + 15 = the weight of the water

Let 18 = total weight of water and pail

Equation: x + x + 15 = 18

Combine terms and solve as before.

Quote:

d) Tweedledum and Tweedledee bought a cake and cut it into 3 pieces, one piece for each of them and one piece for Alice. Tweedledum's piece was 50g heavier than Tweedledee's piece. Tweedledee's piece was 30g heavier than Alice's piece. The total mass was 710g. What was the mass of Alice's piece?

me: That took 2 days. I don't know how to start with this honestly like what method to use. I'm missing a systematic approach to all these.

Thank you
Alice is the one we know nothing about, so we assign our variable to her and state the others in terms of that variable.

Let x = weight of Alice's piece

Let x + 30 = weight of Tweedledee's piece

Let x + 30 + 50 = weight of Tweedledum's piece

Let 710 = Total weight

Equation: x + x + 30 + x + 30 + 50 = 710

Combine terms and solve as before.
• Jun 1st 2009, 09:29 AM
Beginner101
Hey master, thank you very much for helping me! :)

I read your examples just after you posted them, went away for a snack and watch a sci-fi channel to take my mind off this all and now came back to do the examples myself without even peeping at yours. Let's see.

Quote:

a) Demelza's dad is three time as old as Demelza. The sum of their ages is 52. How old is Demelza?
x = unknown = Demelza
3x = unknown = Demelza's Dad

x + 3x = 52
4x = 52
x = 52/4
x = 13 = Demelza's age

52 - x = 3x
52 - 13 = 39 = Demelza's dad's age

Quote:

b) Three consecutive odd numbers add up to 93. Find these numbers.
x = first integer

x + x+2 + x+4 = 93
3x + 6 = 93
3x = 93 - 6
3x = 87
x = 29

29 + 31 + 33 = 93

Hence, numbers are 29, 31, 33

Quote:

c) Jack and Jill went up the hill to fetch a pail of water. The water weighed 15KG more than the pail. The total weight was 18KG. How heavy was the pail?
x = weight of pail

x + 15 = 18
x = 18 - 15
x = 3

Hence, pail is 3KG

Quote:

d) Tweedledum and Tweedledee bought a cake and cut it into 3 pieces, one piece for each of them and one piece for Alice. Tweedledum's piece was 50g heavier than Tweedledee's piece. Tweedledee's piece was 30g heavier than Alice's piece. The total mass was 710g. What was the mass of Alice's piece?
x = Alice's piece

x + x+30 + x+30+50 = 710
3x + 110 = 710
3x = 710 -110
3x = 600
x = 600/3
x = 200 = Alice's cake

Check, by substituting:
x + x+30 + x+30+50 = 710
200 + 200+30 + 200+30+50 = 710

Hence, Alice's cake mass is 200g

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Mr, you taught me more than my teacher's ever done in the whole year and within a few minutes !! (Clapping) (Speechless) (Happy)

Why don't people who can and want to teach do it instead of them? I would be interested then and would learn and make fast progress. Instead they blame us for getting poor marks when all it does it reflect their incompetence at teaching something simple. Something not our fault. 3/4 of my class will fail these coming exams and we're supposed to just shut up.

Why can't I give more thank you's? It should be allowed in such moments I feel. Or maybe not due to stupid spammers gah
• Jun 1st 2009, 10:29 AM
masters
Quote:

Originally Posted by Beginner101
Hey master, thank you very much for helping me! :)

I read your examples just after you posted them, went away for a snack and watch a sci-fi channel to take my mind off this all and now came back to do the examples myself without even peeping at yours. Let's see.

x = weight of pail

x + 15 = 18
x = 18 - 15
x = 3

Hence, pail is 3KG

I must disagree with the above equation. Look at my presentation of this problem in my previous post.

Let x = the weight of the pail. This is what we don't know anything about.

Let x + 15 = the weight of the water. Remember now that the water is 15kg more than the weight of the pail.

Together they weigh 18kg. This gives us the following equation:

x + x + 15 = 18.

We had to add the two expressions together to reach 18kg.

Combine terms

2x + 15 = 18

Subtract 15

2x = 3

Divide by 2

x = 1.5 kg

Let's check. The pail weighs 1.5kg. The water weighs 15kg more than that, so the water weighs 16.5kg. Now, let's add the two together and see if it comes to 18kg.

1.5kg + 16.5kg = 18kg.

It does.

Quote:

Mr, you taught me more than my teacher's ever done in the whole year and within a few minutes !! (Clapping) (Speechless) (Happy)

Why don't people who can and want to teach do it instead of them? I would be interested then and would learn and make fast progress. Instead they blame us for getting poor marks when all it does it reflect their incompetence at teaching something simple. Something not our fault. 3/4 of my class will fail these coming exams and we're supposed to just shut up.

Why can't I give more thank you's? It should be allowed in such moments I feel. Or maybe not due to stupid spammers gah
Some teachers teach well, some pretty good, and some should be doing something else. Regardless, you must persevere. Seek out tutors (as you did here) or other resources (human or otherwise) to get you over the tough spots. When my students tell me that they failed something because of the teacher, my response is 'you should've passed in spite of the teacher'. Look for the resources you need to get you through, other students, different teachers, professional tutor, whatever. Don't despair. You'll come in contact with many good and some excellent instructors along your educational path.