# Question

Just wonder if there is better way of answering this question than using “guess & check” & algebra

There were 612 bicycles & tricycles. Each bicycle had 2 wheels & tricycle had 3. Total no of bicycle wheels was 224 more than the total no of tricycle wheels. Find the diff between the no of bicycle & tricycle.

TIA

Just wonder if there is better way of answering this question than using “guess & check” & algebra

There were 612 bicycles & tricycles. Each bicycle had 2 wheels & tricycle had 3. Total no of bicycle wheels was 224 more than the total no of tricycle wheels. Find the diff between the no of bicycle & tricycle.

EQ1: B + T = 612

EQ2: 2B – 3T = 224

EQ 3 = EQ1 * 2: 2B+2T = 1224

EQ3 – EQ2: 5T = 1000

T = 200

B = 412

Diff = 212

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Just wonder if there is better way of answering this question than using “guess & check” & algebra

There were 612 bicycles & tricycles. Each bicycle had 2 wheels & tricycle had 3. Total no of bicycle wheels was 224 more than the total no of tricycle wheels. Find the diff between the no of bicycle & tricycle.

EQ1: B + T = 612

EQ2: 2B – 3T = 224

EQ 3 = EQ1 * 2: 2B+2T = 1024

EQ3 – EQ2: 5T = 800

T = 160

B = 452

Diff = 292

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Difference = 212

Equation 1: B + T = 612

Equation 2: 2B – 3T = 224

Equation 1 * 2

= Equation 3: 2B + 2T = 1224

Equation 3 – Equation 2

= 5T = 1000

T = 200

Bicycle = 412

Difference = 212

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Let’s analyse….

612 bicycles, 0 tricycle -> wheel diff = (612 x 2) – (0 x 3) = 1224

611 bicycles, 1 tricycle -> wheel diff = (611 x 2) – (1 x 3) = 1219

610 bicycles, 2 tricycles -> wheel diff = (610 x 2) – (2 x 3) = 1214

As you can see, every increase in 1 tricycle, the number of wheel difference decreases by 5.

So from the initial 1224 difference to drop to the target difference of 224, it is a decrease of 1224 – 224 = 1000

Since the decrease rate is 5 per increase of tricycle, there were 1000 / 5 = 200 tricycles.

Number of bicycles -> 612 – 200 = 412

Difference between no. of bicycles & tricycles = 412 – 200 = 212

Check

412 bicycles -> 824 wheels

200 tricycles -> 600 wheels

Difference -> 824 – 600 = 224 (correct)

Model method

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I would solve the question as follows :

224/2 = 112 (bicycles)
612 – 112 = 500 (bicycles and tricycles)
3 bicycles x 2 bicycle wheels = 2 tricycles x 3 tricycle wheels
3 + 2 = 5
500/5 = 100
100 x 3 + 112 = 412 (bicycles)
100 x 2 = 200 (tricycles)
412 – 200 = 212 (more bicycles)

Ans : 212 more bicycles.

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This is a Quantity Amount question.

 Bicycle Tricycle Total Quantity 612 – 1u 1u 612 Each 2 3 Product 1224 – 2u 3u 1224 + 1u

1224 – 2u = 3u + 224

1224 – 224 = 3u + 2u

5u = 1000

1u = 1000 ÷ 5 = 200 Tricycle

612 – 200 = 412  bicycle

412 – 200 = 212

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This is a Quantity Amount question.

 Bicycle Tricycle Total Quantity 612 – 1u 1u 612 Each 2 3 Product 1224 – 2u 3u 1224 + 1u

1224 – 2u = 3u + 224

1224 – 224 = 3u + 2u

5u = 1000

1u = 1000 ÷ 5 = 200 Tricycle

612 – 200 = 412  bicycle

412 – 200 = 212

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Hi, BD’s explanation is great & Acestarling’s Assumption method is fantastic. I had thought in terms of the logic of ratio though, so that I can work with smaller numbers.

224divide2=112 (B)

612-112=500 (B&T, in sets of 5 wheels, 2:3. LCM of 2 & 3 is 6)

5u->500

1u->500divide5=100

(100×3)+112=412B

100×2=200T

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If all 612 is bicycle, total wheel = 612 x 2 = 1224

Therefore, tricycle more than bicycle = 1224

If one bicycle is replaced by one tricycle, total bicycle wheel “reduced” by = 2 + 3 = 5

1224 – 224 = 1000

1000 / 5 = 200

Therefore, number of tricycle = 200

And number of bicycle = 612 – 200 = 412

Answer = 412 – 200 = 212

Check : ( 412 x 2 ) – ( 200 x 3 ) = 224

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