Question

Ruth has 36 vases of flowers. Some of the vases contain 3 daisies. The other vases contain 4 lilacs. There are 125 flowers in the vases in total. How many vases of each type of flower does Ruth have?

Answer 1

• 13 vases of lilacs
• 23 vases of daisies

Explanation:

You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.

Setup

Let x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:

x +y = 36 . . . . . total number of vases

3x +4y = 125 . . . total number of flowers

Solution

Substituting for x, we have ...

x = 36 -y

3(36 -y) +4y = 125

108 +y = 125

y = 13

x = 36 -13 = 23

There are 23 vases of daisies and 13 vases of lilacs.