1.)Four times a certain number is the same as the number increased by 78. Find the number.

2.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike?

3.)Alex is six years older than his sister, Emma. The sum of their ages is 32. How old is Alex?

4.)Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?

5.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?

1)

4n = n + 78
3n = 78
n = 78/3
n = 26

I'll be glad to check your answers for the other problems.

1.) To solve this problem, let's let the certain number be represented by x. According to the problem, four times the certain number (4x) is the same as the number increased by 78 (x + 78).

Setting up the equation:
4x = x + 78

To isolate x, we need to get rid of the x on the right side of the equation. We can do this by subtracting x from both sides.

4x - x = x - x + 78
3x = 78

Next, we need to isolate x by dividing both sides of the equation by 3.

3x/3 = 78/3
x = 26

So, the certain number is 26.

2.) Let's represent the price of the red bike as x. According to the problem, the blue bike is $14 less than the red bike, so its price can be represented as (x - $14).

The sum of their prices is $300, so we can set up the equation:
x + (x - $14) = $300

Combining like terms, we have:
2x - $14 = $300

To isolate x, we need to get rid of the $14 on the left side of the equation. We can do this by adding $14 to both sides.

2x - $14 + $14 = $300 + $14
2x = $314

Next, we need to isolate x by dividing both sides of the equation by 2.

2x/2 = $314/2
x = $157

So, the price of the red bike is $157.

3.) Let's represent Emma's age as x. According to the problem, Alex is six years older than Emma, so his age can be represented as (x + 6). The sum of their ages is 32, so we can set up the equation:

x + (x + 6) = 32

Combining like terms, we have:
2x + 6 = 32

To isolate x, we need to get rid of the 6 on the left side of the equation. We can do this by subtracting 6 from both sides.

2x + 6 - 6 = 32 - 6
2x = 26

Next, we need to isolate x by dividing both sides of the equation by 2.

2x/2 = 26/2
x = 13

So, Emma is 13 years old.

4.) Let's represent Mousy's age as x. According to the problem, Mrs. Computer is 3 times older than her daughter, Mousy, so her age can be represented as (3x). The sum of their ages is 52, so we can set up the equation:

x + (3x) = 52

Combining like terms, we have:
4x = 52

To isolate x, we need to get rid of the 4 on the left side of the equation. We can do this by dividing both sides by 4.

4x/4 = 52/4
x = 13

So, Mousy is 13 years old.

5.) Let's represent Tom's age as x. According to the problem, Mike is 5 years more than twice as old as Tom, so his age can be represented as (2x + 5). The sum of their ages is 65, so we can set up the equation:

x + (2x + 5) = 65

Combining like terms, we have:
3x + 5 = 65

To isolate x, we need to get rid of the 5 on the left side of the equation. We can do this by subtracting 5 from both sides.

3x + 5 - 5 = 65 - 5
3x = 60

Next, we need to isolate x by dividing both sides of the equation by 3.

3x/3 = 60/3
x = 20

So, Tom is 20 years old.

To find Mike's age, we substitute x = 20 into the expression (2x + 5):

2(20) + 5 = 40 + 5 = 45

So, Mike is 45 years old.