Julian grows five different types of flowers in his garden: lilies, crocuses, tulips, daisies, and roses. He picks some flowers from his garden and makes the following observations about the flowers he picked:
There are four more daisies than lilies.
There are twice as many roses as crocuses.
There are half as many tulips as daisies.
There are two fewer lilies than roses.
There are five crocuses.
How many of each type of flower did Julian pick? Justify your answer.
Since we know there are \(5\) crocuses and we know that there are twice as many roses as crocuses, there must be \(5 \times 2 = 10\) roses.
Since we know there are \(10\) roses and we know that there are \(2\) fewer lilies than roses, there must be \(10 - 2 = 8\) lilies.
Since we know there are \(8\) lilies and we know that there are \(4\) more daisies than lilies, there must be \(8 + 4 = 12\) daisies.
Since we know there are \(12\) daisies and we know that there are half as many tulips as daisies, there must be \(12 \div 2 = 6\) tulips.
In summary Julian picked:
\(5\) crocuses, \(10\) roses, \(8\) lilies, \(12\) daisies, and \(6\) tulips.