Felix's Flower Shop ordered 1,080 roses in preparation for Valentine's Day. All of the roses were either red, pink, or white. There were 3 times as many red roses ordered as white roses. The shop ordered twice as many white roses as pink roses.How many red roses did the flower shop order?
Question
Felix's Flower Shop ordered 1,080 roses in preparation for Valentine's Day. All of the roses were either red, pink, or white. There were 3 times as many red roses ordered as white roses. The shop ordered twice as many white roses as pink roses.How many red roses did the flower shop order?
Solution
Let's denote the number of pink roses as P, the number of white roses as W, and the number of red roses as R.
From the problem, we know that:
- The total number of roses is 1080, so P + W + R = 1080.
- There were 3 times as many red roses as white roses, so R = 3W.
- The shop ordered twice as many white roses as pink roses, so W = 2P.
We can substitute the second and third equations into the first to solve for P:
P + 2P + 3(2P) = 1080 P + 2P + 6P = 1080 9P = 1080 P = 1080 / 9 P = 120
Then we can substitute P = 120 into the equation W = 2P to find W:
W = 2 * 120 W = 240
Finally, we substitute W = 240 into the equation R = 3W to find R:
R = 3 * 240 R = 720
So, the flower shop ordered 720 red roses.
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