Question

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?

Desmos Scientific Calculator



(1 point)
Responses

9 cakes
9 cakes

8 1/2
cakes
8 and 1 half cakes

7 1/2
cakes
7 and 1 half cakes

7 6/7
cakes
7 and 6 sevenths cakes
Skip to navigation

Answer 1

are you sure

Answer 2

To calculate the total number of cakes sold, we first need to convert all the mixed fractions into improper fractions and then sum them all 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 cake:**
\[
\frac{3}{4}
\]

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

Now we sum all the cakes sold:

\[
\frac{9}{4} + \frac{5}{2} + \frac{3}{4} + \frac{7}{2}
\]

To add these fractions, we should convert the fractions to a common denominator. The least common multiple of the denominators (4 and 2) is 4. We convert each fraction:

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

Now we can sum them all up:

\[
\frac{9}{4} + \frac{10}{4} + \frac{3}{4} + \frac{14}{4} = \frac{9 + 10 + 3 + 14}{4} = \frac{36}{4} = 9
\]

So the total number of cakes sold is **9 cakes**.

Answer 3

Let's go through the calculations again step by step to confirm the total number of cakes sold.

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 cake:**
\[
\frac{3}{4}
\]

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

Now, we will add these fractions together. To do this, we need a common denominator. The least common multiple of 4 and 2 is 4.

- **Convert red velvet and sugar cream cakes to have the same denominator of 4:**
- \(\frac{5}{2} = \frac{10}{4}\)
- \(\frac{7}{2} = \frac{14}{4}\)

Now we can rewrite the total:

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

Next, we combine the numerators:

\[
\frac{9 + 10 + 3 + 14}{4} = \frac{36}{4} = 9
\]

So the total number of cakes sold is indeed **9 cakes**.