A flower garden has three times as many red roses as pink roses. Twice the number of red roses is equal to four times the number of pink roses increased by ten. How many red roses are there? How many pink roses are there?

15 red roses and 5 pink roses

Let x represent red roses
Let y represent pink roses

2x=4y+10
x=3y

2x=4y+10
2(3y)=4y+10
6y=4y+10
6y-4y=10
2y=10
2y/2=10/2
y=5

x=3p
x=3(5)
x=15

Therefore, there are 15 red roses and 5 pink roses

To solve this problem, let's assign variables to the unknown quantities. Let's call the number of pink roses "x" and the number of red roses "y".

According to the problem, the flower garden has three times as many red roses as pink roses. So we can say that:
y = 3x ...(Equation 1)

The problem also states that twice the number of red roses is equal to four times the number of pink roses increased by ten. So we can write this as:
2y = 4x + 10 ...(Equation 2)

Now we have a system of two equations with two variables. We can solve this system using substitution or elimination. Let's use substitution:

Since Equation 1 is already solved for "y", we can substitute it into Equation 2:
2(3x) = 4x + 10

Simplifying the equation:
6x = 4x + 10
2x = 10
x = 5

Now we can substitute the value of "x" back into Equation 1 to find the value of "y":
y = 3(5)
y = 15

Therefore, there are 15 red roses and 5 pink roses in the flower garden.

there are 1 red roses and two pink roses

x = red roses

y = pink roses

y = 3y
2x = 4y + 10

solve the system for your answer