Question

Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke 20 minutes more than he practices the butterfly stroke.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)

Part B: How much time does Ted spend on practicing the breaststroke every day? (3 points)

Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke every day? Explain your reasoning. (2 points)

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Answer 1

Answer:

Let the three consecutive positive integers be n, n+1 and n+2.

Whenever a number is divided by 3, the remainder obtained is either 0,1 or 2.

Therefore, n=3p or 3p+1 or 3p+2, where p is some integer.

If n=3p, then n is divisible by 3.

If n=3p+1, then n+2=3p+1+2=3p+3=3(p+1) is divisible by 3.

If n=3p+2, then n+1=3p+2+1=3p+3=3(p+1) is divisible by 3.

So, we can say that one of the numbers among n,n+1 and n+2 is always divisible by 3 that is:

n(n+1)(n+2) is divisible by 3.

Similarly, whenever a number is divided by 2, the remainder obtained is either 0 or 1.

Therefore, n=2q or 2q+1, where q is some integer.

If n=2q, then n and n+2=2q+2=2(q+1) is divisible by 2.

If n=2q+1, then n+1=2q+1+1=2q+2=2(q+1) is divisible by 2.

So, we can say that one of the numbers among n, n+1 and n+2 is always divisible by 2.

Since, n(n+1)(n+2) is divisible by 2 and 3.

Hence, n(n+1)(n+2) is divisible by 6.

Step-by-step explanation:

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Answer 2

Answer:

We get that:

1. Linear equation is x + y = 50
2. Ted spends 35 minutes on practicing the breaststroke every day.
3. No, it is not possible for Ted to have spent 45 minutes practicing the butterfly stroke every day because of the time constraint.

Step-by-step explanation:

Total time of practicing = 50 minutes

Let the time for practicing butterfly stroke be x

And for break stroke be y

ATQ:

x + y = 50   ... (1)

Also,

x + 20 = y    ...(2)

Substituting (2) in (1), we get that:

x + (x + 20) = 50

2x + 20 = 50

2x = 50 - 20

2x = 30

x  =30 / 2

x  = 15

y = 15 + 20  =35 minutes

No, it is not possible for Ted to practice butterfly stroke for 45 minutes every day as he needs to practice the break stroke for 20 more minutes than butterfly stroke and he has a time constraint.

Therefore, we get that:

1. Linear equation is x + y = 50
2. Ted spends 35 minutes on practicing the breaststroke every day.
3. No, it is not possible for Ted to have spent 45 minutes practicing the butterfly stroke every day because of the time constraint.

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