Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4 chocolate cakes, 2 1/2 red velvet cakes, 3/4 of a carrot cake and 3 1/2 sugar cream cakes. What is the total number of cakes sold?

Question

Desmos Scientific Calculator

Answer 1

To find the total number of cakes sold, we will first convert all quantities of cake sold into improper fractions and then sum them up.

1. Chocolate cakes: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

2. Red velvet cakes: \[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]

3. Carrot cakes: \[ \frac{3}{4} \]

4. Sugar cream cakes: \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \]

Now, we will sum these fractions together:

\[ \text{Total number of cakes} = \frac{9}{4} + \frac{5}{2} + \frac{3}{4} + \frac{7}{2} \]

To add these fractions, we need a common denominator. The least common multiple of 4 and 2 is 4.

Now, we convert the fractions to have this common denominator:

• \(\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}\)
• \(\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}\)

Now, we can rewrite the addition:

\[ \frac{9}{4} + \frac{10}{4} + \frac{3}{4} + \frac{14}{4} \]

Now, we add the numerators:

\[ 9 + 10 + 3 + 14 = 36 \]

Thus, the total becomes:

\[ \frac{36}{4} = 9 \]

Therefore, the total number of cakes sold is 9 cakes.