Question

ava flipped through a dessert cookbook with cookie recipes from around the world. she picked out some favorites and recorded the amount of milk used in each.
use the line plot to answer the question below.
amount of milk
cups
if you combine all the milk from the recipes with exactly $1 \frac{7}{8}$ cups of milk, how much milk will you have in all?
write your answer as a fraction, mixed number, or whole number.
\boxed{} cups

Explanation:

Step1: Calculate milk from line plot

First, we identify the number of x's at each amount:
- At \(1\) cup: \(1\) x
- At \(1\frac{1}{4}\) cups: \(1\) x
- At \(1\frac{5}{8}\) cups: \(2\) x's
- At \(1\frac{3}{4}\) cups: \(2\) x's
- At \(1\frac{7}{8}\) cups: \(2\) x's
- At \(2\) cups: \(1\) x

Now, convert each mixed number to an improper fraction:
- \(1=\frac{8}{8}\)
- \(1\frac{1}{4}=\frac{5}{4}=\frac{10}{8}\)
- \(1\frac{5}{8}=\frac{13}{8}\)
- \(1\frac{3}{4}=\frac{7}{4}=\frac{14}{8}\)
- \(1\frac{7}{8}=\frac{15}{8}\)
- \(2=\frac{16}{8}\)

Calculate total milk from recipes:
\[ \begin{align*} &1\times\frac{8}{8}+1\times\frac{10}{8}+2\times\frac{13}{8}+2\times\frac{14}{8}+2\times\frac{15}{8}+1\times\frac{16}{8}\\ =&\frac{8}{8}+\frac{10}{8}+\frac{26}{8}+\frac{28}{8}+\frac{30}{8}+\frac{16}{8}\\ =&\frac{8 + 10+26 + 28+30 + 16}{8}\\ =&\frac{118}{8}\\ =&\frac{59}{4}=14\frac{3}{4} \end{align*} \]

Step2: Add \(1\frac{7}{8}\) cups

Convert \(1\frac{7}{8}\) to improper fraction: \(1\frac{7}{8}=\frac{15}{8}\)

Now add to the total from recipes:
\[ \begin{align*} \frac{59}{4}+\frac{15}{8}&=\frac{118}{8}+\frac{15}{8}\\ &=\frac{118 + 15}{8}\\ &=\frac{133}{8}\\ &=16\frac{5}{8} \end{align*} \]

Wait, maybe I misread the problem. Wait, the problem says "combine all the milk from the recipes with exactly \(1\frac{7}{8}\) cups of milk". Wait, maybe first find total from recipes:

Wait, let's re - examine the line plot:

Looking at the line plot:

- \(1\) cup: 1 x
- \(1\frac{1}{4}\) cup: 1 x
- \(1\frac{5}{8}\) cup: 2 x's
- \(1\frac{3}{4}\) cup: 2 x's
- \(1\frac{7}{8}\) cup: 2 x's
- \(2\) cup: 1 x

Let's calculate the total milk from the recipes (sum of all amounts):

For \(1\) cup: \(1\times1 = 1\)

For \(1\frac{1}{4}\) cup: \(1\times1\frac{1}{4}=1\frac{1}{4}\)

For \(1\frac{5}{8}\) cup: \(2\times1\frac{5}{8}=2\times\frac{13}{8}=\frac{26}{8}=3\frac{2}{8}=3\frac{1}{4}\)

For \(1\frac{3}{4}\) cup: \(2\times1\frac{3}{4}=2\times\frac{7}{4}=\frac{14}{4}=3\frac{2}{4}=3\frac{1}{2}\)

For \(1\frac{7}{8}\) cup: \(2\times1\frac{7}{8}=2\times\frac{15}{8}=\frac{30}{8}=3\frac{6}{8}=3\frac{3}{4}\)

For \(2\) cup: \(1\times2 = 2\)

Now sum these up:

\[ \begin{align*} &1+1\frac{1}{4}+3\frac{1}{4}+3\frac{1}{2}+3\frac{3}{4}+2\\ =&(1 + 2)+(1\frac{1}{4}+3\frac{1}{4}+3\frac{3}{4})+3\frac{1}{2}\\ =&3+(7\frac{5}{4})+3\frac{1}{2}\\ =&3 + 8\frac{1}{4}+3\frac{1}{2}\\ =&(3 + 8+3)+(\frac{1}{4}+\frac{1}{2})\\ =&14+\frac{3}{4}\\ =&14\frac{3}{4} \end{align*} \]

Now add \(1\frac{7}{8}\) to \(14\frac{3}{4}\):

Convert \(14\frac{3}{4}\) to eighths: \(14\frac{3}{4}=14\frac{6}{8}\)

\(14\frac{6}{8}+1\frac{7}{8}=15\frac{13}{8}=16\frac{5}{8}\)

Wait, maybe the problem is simpler. Wait, maybe the "all the milk from the recipes" is the sum of the amounts, and then add \(1\frac{7}{8}\).

Alternatively, maybe I made a mistake in counting. Let's count the number of x's and multiply by the amount:

- \(1\) cup: 1 x \(\Rightarrow1\times1 = 1\)
- \(1\frac{1}{4}\) cup: 1 x \(\Rightarrow1\times1\frac{1}{4}=1\frac{1}{4}\)
- \(1\frac{5}{8}\) cup: 2 x's \(\Rightarrow2\times1\frac{5}{8}=3\frac{1}{4}\)
- \(1\frac{3}{4}\) cup: 2 x's \(\Rightarrow2\times1\frac{3}{4}=3\frac{1}{2}\)
- \(1\frac{7}{8}\) cup: 2 x's \(\Rightarrow2\times1\frac{7}{8}=3\frac{3}{4}\)
- \(2\) cup: 1 x \(\Rightarrow1\times2 = 2\)

Now sum these:

\(1+1\frac{1}{4}=2\frac{1}{4}\)

\(2\frac{1}{4}+3\frac{1}{4}=5\frac{2}{4}=5\frac{1}{2}\)

\(5\frac{1}{2}+3\frac{1}{2}=9\)

\(9 + 3\frac{3}{4}=12\frac{3}{4}\)

\(12\frac{3}{4}+2=14\frac{3}{4}\)

Now add \(1\frac{7}{8}\):

\(14\frac{3}{4}+1\frac{7}{8}=14\frac{6}{8}+1\frac{7}{8}=15\frac{13}{8}=16\frac{5}{8}\)

Wait, maybe the problem is that the "all the milk from the recipes" is the sum, and then we add \(1\frac{7}{8}\). But let's check again.

Wait, the line plot:

- \(1\) : 1
- \(1\frac{1}{4}\) : 1
- \(1\frac{5}{8}\) : 2
- \(1\frac{3}{4}\) : 2
- \(1\frac{7}{8}\) : 2
- \(2\) : 1

Let's calculate the sum of the amounts:

\(1\times1+1\times1\frac{1}{4}+2\times1\frac{5}{8}+2\times1\frac{3}{4}+2\times1\frac{7}{8}+1\times2\)

\(=1 + 1\frac{1}{4}+3\frac{1}{4}+3\frac{1}{2}+3\frac{3}{4}+2\)

Group the whole numbers and the fractions:

Whole numbers: \(1 + 1+3+3+3+2=13\)

Fractions: \(\frac{1}{4}+\frac{1}{4}+\frac{1}{2}+\frac{3}{4}=\frac{1 + 1+2 + 3}{4}=\frac{7}{4}=1\frac{3}{4}\)

Total from recipes: \(13 + 1\frac{3}{4}=14\frac{3}{4}\)

Now add \(1\frac{7}{8}\):

\(14\frac{3}{4}+1\frac{7}{8}=14\frac{6}{8}+1\frac{7}{8}=15\frac{13}{8}=16\frac{5}{8}\)

But maybe I misread the problem. Wait, the problem says "combine all the milk from the recipes with exactly \(1\frac{7}{8}\) cups of milk". So the total milk is the sum of the milk from the recipes plus \(1\frac{7}{8}\).

Answer:

\(16\frac{5}{8}\)