Certainly! Let's determine the fraction of the flowers in the bouquet that are daffodils.
1. Calculate the total number of flowers in the bouquet:
The ratio of lilies to daffodils to marigolds is given as [tex]\(7:6:2\)[/tex]. To find the total number of flowers, we add these ratios together:
[tex]\[
\text{Total number of flowers} = 7 + 6 + 2 = 15
\][/tex]
2. Determine the fraction of the flowers that are daffodils:
The number of daffodils is given by the second number in the ratio, which is 6. Therefore, the fraction of the flowers that are daffodils is:
[tex]\[
\text{Fraction of daffodils} = \frac{6}{15}
\][/tex]
3. Simplify the fraction:
To simplify the fraction [tex]\(\frac{6}{15}\)[/tex], we need to find the greatest common divisor (GCD) of 6 and 15. The GCD of 6 and 15 is 3. We then divide the numerator and the denominator by this GCD:
[tex]\[
\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}
\][/tex]
Thus, the fraction of the flowers in the bouquet that are daffodils is [tex]\(\frac{2}{5}\)[/tex].
