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)

Let x = the first odd integer

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 + 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.

Let x = weight of the pailc) 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 + 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.

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

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.