Question
An ice cream shop uses a mix of blueberries and cherries on its ice cream sundaes. The shop has
5 3/4 pounds of blueberries and
4 1/2 of cherries. The shop mixes the blueberries and cherries and uses
1/16 pound of the mix on each sundae. Which expression represents the total number of sundaes that the shop can make using all of the blueberries and cherries?
A
(534÷116)+412\left(5\frac{3}{4}\div \frac{1}{16}\right)+4\frac{1}{2}(5
4
3
÷
16
1
)+4
2
1
B
534+(412÷116)5\frac{3}{4}+\left(4\frac{1}{2}\div \frac{1}{16}\right)5
4
3
+(4
2
1
÷
16
1
)
C
116÷(534+412)\frac{1}{16}\div \left(5\frac{3}{4}+4\frac{1}{2}\right)
16
1
÷(5
4
3
+4
2
1
)
D
(534+412)÷116\left(5\frac{3}{4}+4\frac{1}{2}\right)\div \frac{1}{16}(5
4
3
+4
2
1
)÷
16
1
Answers
GPT-4o mini
To determine the total number of sundaes that the shop can make using all of the blueberries and cherries, we need to first find the total weight of the blueberries and cherries combined, and then divide that by the weight used per sundae.
1. **Convert the weights to improper fractions**:
- Blueberries: \( 5 \frac{3}{4} = \frac{23}{4} \) pounds
- Cherries: \( 4 \frac{1}{2} = \frac{9}{2} = \frac{18}{4} \) pounds
2. **Add the weights together**:
\[
\text{Total weight} = \frac{23}{4} + \frac{18}{4} = \frac{41}{4} \text{ pounds}
\]
3. **Weight used per sundae**: \( \frac{1}{16} \) pound
4. **Calculate the total number of sundaes**:
\[
\text{Number of sundaes} = \frac{\text{Total weight}}{\text{Weight per sundae}} = \frac{\frac{41}{4}}{\frac{1}{16}} = \frac{41}{4} \times 16 = \frac{41 \times 16}{4} = \frac{656}{4} = 164
\]
Now, let's find the appropriate expression from the options given.
- To represent the total number of sundaes mathematically, we would want a representation of:
\[
\left(5 \frac{3}{4} + 4 \frac{1}{2}\right) \div \frac{1}{16} = \left(\frac{41}{4}\right) \div \frac{1}{16}
\]
This matches the operation done in Option D.
Thus, the correct option representing the total number of sundaes that the shop can make using all of the blueberries and cherries is:
**D: \((5 \frac{3}{4} + 4 \frac{1}{2}) \div \frac{1}{16}\)**.
1. **Convert the weights to improper fractions**:
- Blueberries: \( 5 \frac{3}{4} = \frac{23}{4} \) pounds
- Cherries: \( 4 \frac{1}{2} = \frac{9}{2} = \frac{18}{4} \) pounds
2. **Add the weights together**:
\[
\text{Total weight} = \frac{23}{4} + \frac{18}{4} = \frac{41}{4} \text{ pounds}
\]
3. **Weight used per sundae**: \( \frac{1}{16} \) pound
4. **Calculate the total number of sundaes**:
\[
\text{Number of sundaes} = \frac{\text{Total weight}}{\text{Weight per sundae}} = \frac{\frac{41}{4}}{\frac{1}{16}} = \frac{41}{4} \times 16 = \frac{41 \times 16}{4} = \frac{656}{4} = 164
\]
Now, let's find the appropriate expression from the options given.
- To represent the total number of sundaes mathematically, we would want a representation of:
\[
\left(5 \frac{3}{4} + 4 \frac{1}{2}\right) \div \frac{1}{16} = \left(\frac{41}{4}\right) \div \frac{1}{16}
\]
This matches the operation done in Option D.
Thus, the correct option representing the total number of sundaes that the shop can make using all of the blueberries and cherries is:
**D: \((5 \frac{3}{4} + 4 \frac{1}{2}) \div \frac{1}{16}\)**.