A person is 3 times as old as aonther person but in 15 years she will only be 2 times as old. I found the answer the younger person is 15 years old and the older person is 45 years old. But 15 years from now the younger person will be 30 years old and the older person will be 60 years old. I have to come up with an equation for this. I wanted to say y=15x+30 where x is the number of times that the person is older than the younger person and y is the final number of years older. But this doubles the answer and also is totally wrong. Please help.

Question

A person is 3 times as old as aonther person but in 15 years she will only be 2 times as old. I found the answer the younger person is 15 years old and the older person is 45 years old. But 15 years from now the younger person will be 30 years old and the older person will be 60 years old. I have to come up with an equation for this. I wanted to say y=15x+30 where x is the number of times that the person is older than the younger person and y is the final number of years older. But this doubles the answer and also is totally wrong. Please help.

Answer 1

You got the right answer without using equations. Here is the way to do it with algebra. Let x be the younger person's age now, and y be the older person's age now.

y = 3x
(y + 15) = 2(x + 15)

Now eliminate one variable using algebra.

y = 2x +30 -15 = 2x + 15
3x = 2x + 15
x = 15.

Answer 2

solve austy is 22 years older than boboy in 2 years austy will be three times as old as she boboy .how old are they now ?pls solved

Answer 3

To come up with an equation, let's break down the problem step-by-step:

1. Let's assume the younger person's age is represented by 'y'.
2. Since the older person is 3 times as old, their age can be represented as '3y'.
3. In 15 years, the younger person's age will be 'y + 15' and the older person's age will be '3y + 15'.
4. According to the problem, in 15 years, the older person will only be 2 times as old as the younger person, so we can set up the equation:

3y + 15 = 2(y + 15)

Now, let's solve the equation step-by-step:

1. Distribute the 2 on the right side of the equation:

3y + 15 = 2y + 30

2. Move all the terms involving 'y' to the left side of the equation and the constants to the right side:

3y - 2y = 30 - 15

y = 15

Thus, the value of 'y' is 15, which represents the younger person's age.

To find the older person's age, we substitute 'y = 15' into the equation '3y':

Older person's age = 3 * 15 = 45

So, the younger person is 15 years old and the older person is 45 years old, which matches your initial answer.

Answer 4

To set up the equation correctly, let's assume the age of the younger person is represented by "x" years.

According to the problem, the older person is 3 times as old as the younger person. Therefore, the age of the older person would be "3x" years.

Now, it is given that in 15 years, the older person will be 2 times as old as the younger person. So, the age of the younger person after 15 years would be "x + 15" years, and the age of the older person after 15 years would be "3x + 15" years.

Hence, we can set up the equation as follows:

3x + 15 = 2(x + 15)

Simplifying this equation will help us find the value of "x" which represents the age of the younger person.

Let's solve the equation step by step:

3x + 15 = 2x + 30 (Distribute 2 to x and 15)

3x - 2x = 30 - 15 (Combine like terms)

x = 15 (Simplify both sides)

Therefore, the age of the younger person is 15 years.

To find the age of the older person, substitute the value of "x" into "3x":

3(15) = 45

Hence, the age of the older person is 45 years.

It's important to note that 15 years from now, the younger person will indeed be 30 years old and the older person will be 60 years old. However, when constructing the equation, we consider the current ages of the individuals and set up the equation based on the information provided.