Finding Number of Croissants in a Bakery

A bakery sells three types of pastries: croissants, danishes, and muffins. The ratio of croissants to danishes is 3:2, and the ratio of danishes to muffins is 4:5. If the bakery made a total of 120 pastries, how many croissants did they make?

Let the number of croissants be represented as $C$, danishes as $D$, and muffins as $M$.

From the given ratios, we can express $D$ in terms of $C$ as follows:

$D = \f\frac{2}{3}C$

From the second ratio, we can express $M$ in terms of $D$:

$M = \f\frac{5}{4}D$

Once we substitute for $D$ in terms of $C$, we can write $M$ as:

$M = \f\frac{5}{4} \left( \f\frac{2}{3}C \right)$

Substituting these into the total pastries gives us the equation: $C + D + M = 120$.