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?
just write the words as algebra:
r = 3p
2r = 4p+10
now do the math
To solve this problem, let's set up equations using the given information.
Let's assume the number of pink roses is "x".
According to the problem, the number of red roses is three times the number of pink roses, which gives us: number of red roses = 3x.
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 the equation as:
2 * (number of red roses) = 4 * (number of pink roses) + 10.
Substituting the values we derived earlier:
2 * (3x) = 4 * x + 10.
Simplifying the equation:
6x = 4x + 10,
2x = 10.
To find the value of "x" (number of pink roses), we solve the equation:
2x = 10,
x = 5.
So, there are 5 pink roses.
To find the number of red roses, we substitute the value of "x" into the equation for red roses:
Number of red roses = 3 * x = 3 * 5 = 15.
Therefore, there are 15 red roses in the garden.