Question

Yellow paint plus blue paint equals 180 bottles of paint. There are 25 more bottles of blue paint than yellow paint. How many of each are there?

Answer 1

Remember it has to equal up to 180

Answer 2

There does not have to be a whole number

Answer 3

Bob is hiking down a 12-mile country trail. He could hike 3mph for the first two hours and hike five mph the rest of the way, or he could just hike 4mph the whole way. How long would each option take?

Answer 4

Let's say there are x bottles of yellow paint.
The number of bottles of blue paint is 'x+25'
The total number of bottles is x+x+25 = 2x+25 = 180 bottles
2x=180-25
2x=155
x=77.5 bottles
There are 77 yellow paint bottles and 77+25=<<77+25=102>>102 blue paint bottles. Answer: \boxed{77,102}.

Answer 5

Apologies for the error. Let's correct the calculation:

Let's say there are x bottles of yellow paint.
The number of bottles of blue paint is equal to x + 25.

The total number of paint bottles is yellow + blue = x + (x + 25) = 180 bottles.

Combining like terms, we have 2x + 25 = 180.

Subtracting 25 from both sides, we get 2x = 155.

Dividing both sides by 2, we find that x = 77.5.

Since the solution must be a whole number, it means that there is a mistake in the problem statement since we cannot have a non-integer number of paint bottles.

Answer 6

Apologies for the misunderstanding. In that case, we can proceed with the calculation using the equation:

x + (x + 25) = 180

Combining like terms, we have:

2x + 25 = 180

Subtracting 25 from both sides, we get:

2x = 155

Dividing both sides by 2, we find that:

x = 77.5

Therefore, there are 77.5 bottles of yellow paint and 77.5 + 25 = 102.5 bottles of blue paint.

Answer 7

Let's first calculate the time it would take if Bob hikes at 3 mph for the first two hours and then at 5 mph for the rest of the trail.

For the first two hours at 3 mph, Bob covers a distance of 2 hours * 3 mph = 6 miles.

He has 12 - 6 = <<12-6=6>>6 miles remaining to hike at 5 mph.

To cover 6 miles at 5 mph, it would take Bob 6 miles / 5 mph = 1.2 hours.

So, in total, this option would take Bob 2 + 1.2 = 3.2 hours.

Now let's calculate the time it would take if Bob hikes at a constant speed of 4 mph for the entire trail.

To cover a distance of 12 miles at 4 mph, it would take Bob 12 miles / 4 mph = 3 hours.

Therefore, if Bob hikes at 3 mph for the first two hours and 5 mph for the rest of the trail, it would take him 3.2 hours.
However, if he hikes at a constant speed of 4 mph for the entire trail, it would take him 3 hours.

Hence, the second option of hiking at a constant speed of 4 mph would be faster, taking 3 hours.