Yesterday, The Coffee Spot sold $10\frac{5}{8}$ carafes of caffeinated coffee and $9\frac{7}{8}$ carafes of decaffeinated coffee. How many carafes of coffee did they sell in all? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ $\_\_\_\_$ carafes

Full solution

Q. Yesterday, The Coffee Spot sold

10\frac{5}{8}

carafes of caffeinated coffee and

9\frac{7}{8}

carafes of decaffeinated coffee. How many carafes of coffee did they sell in all?

\newline

Write your answer as a fraction or as a whole or mixed number.

\newline

\_\_\_\_

carafes

Identify amounts sold: Step $1$ : Identify the amounts sold of each type of coffee. $\newline$ Caffeinated coffee sold: $10\frac{5}{8}$ carafes. $\newline$ Decaffeinated coffee sold: $9\frac{7}{8}$ carafes.
Convert to improper fractions: Step $2$ : Convert mixed numbers to improper fractions for easier addition. $\newline$ $10 \frac{5}{8} = (10\times8 + 5)/8 = \frac{85}{8}$ . $\newline$ $9 \frac{7}{8} = (9\times8 + 7)/8 = \frac{79}{8}$ .
Add fractions: Step $3$ : Add the two improper fractions. $\newline$ $\frac{85}{8} + \frac{79}{8} = \frac{85 + 79}{8} = \frac{164}{8}$ .
Simplify fraction: Step $4$ : Simplify the fraction. $\frac{164}{8} = 20 \frac{4}{8}$ ; $\frac{4}{8}$ can be simplified to $\frac{1}{2}$ . Final answer: $20 \frac{1}{2}$ carafes.