Question

A florist ordered a shipment of red, blue, and white flowers to use for table decorations at a banquet.

The ratio of red : blue : white flowers in the shipment is
.
There are 60 white flowers in the shipment.
What is the total number of flowers in the shipment?

Answer 1

To find the total number of flowers in the shipment, let’s denote the ratio of red, blue, and white flowers as \( r : b : w \).

Given that there are 60 white flowers, we can express the number of white flowers (\( w \)) in terms of the ratio:

\[
w = 60
\]

From the ratio \( r : b : w \), if we let the ratio be represented in terms of a common variable \( k \), we can write:

\[
r = rk, \quad b = bk, \quad w = wk
\]

Substituting the number of white flowers, we have:

\[
w = 60 \implies wk = 60
\]

To find \( k \), we need to know \( w \) in the ratio.

Now, rearranging gives:

\[
k = \frac{60}{w}
\]

The total number of flowers in the shipment can be calculated as:

\[
\text{Total} = r + b + w = rk + bk + wk
\]

Substituting \( wk = 60 \) directly into the total calculation gives:

\[
\text{Total} = rk + bk + 60
\]

To find \( r \) and \( b \) we need to use the provided ratio and calculate \( r \) and \( b \) accordingly.

Let’s denote the ratio as follows:

1. Assume \( r : b : w = a : b : 1 \) (a simplified form, where we normalize \( w \) to 1).
2. Then \( w = 60 \implies k = 60 \) (indicating there are 60 instances of '1' in the ratio).
3. Therefore, \( r = a \times 60 \) and \( b = b \times 60 \).

Thus, our flowers become:

\[
\text{Total} = (a \cdot 60) + (b \cdot 60) + 60 = 60(a + b + 1)
\]

The total number of flowers thus depends on the sum of \( a + b + 1 \).

Please provide the specific ratio of red to blue to white flowers you would have mentioned earlier, and then we can calculate \( a + b + 1 \) directly.