Question

Elyse and Jamir each make lemonade. Elyse mixes 1
7
3
​
cups of water with
2
1
​
cups of lemonade concentrate. Jamir mixes 1
3
1
​
cups of water with
5
2
​
cups of lemonade concentrate. Which lemonade has a more lemony taste?
Start by finding the unit rate for Elyse’s recipe. You need to find the number of cups of lemonade concentrate per 1 cup of water. What can you divide 1
7
3
​
cups of water by to find 1 cup of water?
Elyse's Lemonade Recipe
÷
1

3
7
Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1 ?
Good work!
To keep the ratio equivalent, you need to divide
2
1
​
by 1
7
3
​
also. How many cups of lemonade concentrate does Elyse’s recipe need for 1 cup of water? Solve
2
1
​
÷ 1
7
3
​
on paper, then enter your answer on Zearn.
Elyse's Lemonade Recipe
÷ 1
7
3
​

÷ 1
7
3
​

Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1

Answer 1

To find the unit rate for Elyse's lemonade recipe, we need to determine the amount of lemonade concentrate per 1 cup of water.

Elyse's Recipe:
- Water: \(1 \frac{7}{3}\) cups
- Lemonade Concentrate: \(2 \frac{1}{2}\) cups

First, we convert the mixed numbers into improper fractions:

1. **Convert \(1 \frac{7}{3}\) (water)**:
\[
1 \frac{7}{3} = \frac{3 \times 1 + 7}{3} = \frac{3 + 7}{3} = \frac{10}{3}
\]

2. **Convert \(2 \frac{1}{2}\) (lemonade concentrate)**:
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
\]

Now, we need to divide the amount of lemonade concentrate by the amount of water to find out how much concentrate is needed for 1 cup of water:

\[
\text{Lemonade Concentrate per 1 cup of Water} = \frac{5/2}{10/3}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
\frac{5}{2} \times \frac{3}{10} = \frac{5 \times 3}{2 \times 10} = \frac{15}{20} = \frac{3}{4}
\]

So, **Elyse's recipe** requires **\(\frac{3}{4}\) cups of lemonade concentrate for 1 cup of water**.

Now let's check Jamir's recipe to see how it compares.

Jamir's Recipe:
- Water: \(1 \frac{3}{1}\) (which is simply 3 cups)
- Lemonade Concentrate: \(5 \frac{2}{1}\) (which is simply 5 cups)

Now, we will again convert this to improper fractions:

1. **Convert \(3\) to an improper fraction** (it is already a whole number):
\[
3 = \frac{3}{1}
\]

2. **Convert \(5\) to an improper fraction** (it is already a whole number):
\[
5 = \frac{5}{1}
\]

Now we will find the concentrate per 1 cup of water for Jamir's recipe:

\[
\text{Lemonade Concentrate per 1 cup of Water} = \frac{5/1}{3/1} = \frac{5}{3}
\]

Now we compare the two:

- Elyse’s recipe provides \(\frac{3}{4}\) cups of concentrate per 1 cup of water.
- Jamir’s recipe provides \(\frac{5}{3}\) cups of concentrate per 1 cup of water.

To compare, we can convert both to decimals for easier comparison:

1. \(\frac{3}{4} = 0.75\)
2. \(\frac{5}{3} \approx 1.67\)

**Conclusion**: **Jamir’s lemonade has a more lemony taste**, with approximately \(1.67\) cups of concentrate per cup of water, compared to Elyse’s \(0.75\) cups of concentrate per cup of water.