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Five years ago, Tom was one third as old as his father was then.In 5 years, Tom will be half as old as his father will be then.

sleet_krkn [62]

Answer:

The father is 35years old and the son Tom is 15years old

Step-by-step explanation:

Let the father's be y

Let Tom's age be T

5 years ago:

The father's age is: y — 5

Tom's age:

T— 5.

But Tom's age was one third the father's age. This is written as:

T — 5 = 1/3(y — 5)

3(T — 5) = y — 5

3T — 15 = y — 5

3T — y = — 5 + 15

3T — y = 10 (1)

In 5years time:

The father's age is:

y + 5

Tom's age:

T + 5

But in 5years time, Tom will be half as old as his father. This is written as:

T + 5 = 1/2(y + 5)

2(T + 5) = y + 5

2T + 10 = y + 5

2T — y = 5 — 10

2T — y = — 5 (2)

Therefore, the equations are

3T — y = 10 (1)

2T — y = — 5. (2)

Solving by elimination method:

Subtract equation (2) from (1)

3T — y = 10

— (2T — y = — 5)

T = 15

Substituting the value of T into equation (1)

3T — y = 10

3(15) — y = 10

45 — y = 10

45 — 10 = y

y = 35

Therefore,

The father is 35years old and the son Tom is 15years old

5 0

4 years ago

Two numbers have these properties:

Elina [12.6K]

The two numbers are 12 and 30

Step-by-step explanation:

Let us revise the meaning of HCF (highest common factor) and LCM (least common multiple)

The highest common factor of two numbers is the largest whole number which is a factor of both, the HCF of 4 and 6 is 2 because the factors of 4 are 1, 2, 4 and the factors of 6 are 1, 2, 3, 6; the common factors are 1, 2 and the greatest is 2 so the highest common factor of 4 , 6 is 2
The least common multiple of two numbers is the smallest number that they both divide evenly into, the least common multiple of 4 and 6 is 12 because the multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, 24, ...; the first common multiple between then is 12

∵ Both numbers are greater than 6

∵ Their HCF is 6

- That means 6 is a factor of both of them

∴ The two numbers are multiple of 6 without any other common

factor greater than 6

Let us write the multiple of 6 greater than 6

∵ 12 , 18 , 24 , 30 , 36 , ......... are multiples of 6

∵ Their LCM is 60

- That means 60 can divided by them

∵ 60 can divided by 12

∵ 60 can divided by 30

∵ The factors of 12 are 1 , 2 , 3 , 4 , 6 , 12

∵ The factor of 30 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30

∵ Their common factors are 1 , 2 , 3 , 6 and the greatest one is 6

- 12 and 30 have HCF of 6 and LCM of 60

∴ The two numbers are 12 and 30

The two numbers are 12 and 30

Learn more:

You can learn more about the factors in brainly.com/question/5194236

#LearnwithBrainly

4 0

4 years ago

Find m<2 and m<3 in the rhombus. The diagram is not to scale.

Umnica [9.8K]

Answer:

m∠2 = 118, and m∠3 = 31

Step-by-step explanation:

The 2 opposite angles of a rhombus are equal.

Angle 1 and Angle 2 are opposite to each other. Since Angle 1 is 118, angle 2 is also 118.

Now looking at the bottom triangle in the rhombus, the two sides are equal (given by 2 lines). Hence, the 2 opposite angles are equal. Since we know 3 angles of a triangle add up to 180 degrees, we can write: (let angle 3 be x):

x + x + 118 = 180

2x = 180 - 118

2x = 62

x = 62/2

x = 31

So m∠2 = 118, and m∠3 = 31

5 0

4 years ago

What is the square root of 8374

Rainbow [258]

<span>91.5095623419 is the answer</span>

7 0

4 years ago

The coefficients in the expansion of (x+y)5 are

alexgriva [62]

Answer:

i believe 5 is the coefficient as the coefficient is always then number thats in the expression next to the variables

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers