the line plot shows the part of a gallon of water that jill drank each day last week. how many gallons of…

the line plot shows the part of a gallon of water that jill drank each day last week. how many gallons of water did jill drink? water drunk 0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1 3 3/8 gallons 3 1/8 gallons 2 1/8 gallons 2 7/8 gallons

Answer

Explanation:

Step1: Identify counts per fraction

$\frac{1}{4}$: 3 X's (since $\frac{1}{4}=\frac{2}{8}$? Wait, no, the x-axis labels: $\frac{1}{8}$, $\frac{1}{4}$ (which is $\frac{2}{8}$? Wait, no, the labels are $\frac{1}{8}$, $\frac{1}{4}$, $\frac{3}{8}$, $\frac{1}{2}$ ( $\frac{4}{8}$ ), $\frac{5}{8}$, $\frac{3}{4}$ ( $\frac{6}{8}$ ), $\frac{7}{8}$. Wait, looking at the line plot:
$\frac{1}{4}$ (position 2): 3 X's? Wait no, the X's: first column ( $\frac{1}{4}$? Wait the x-axis is labeled 0, $\frac{1}{8}$, $\frac{1}{4}$, $\frac{3}{8}$, $\frac{1}{2}$, $\frac{5}{8}$, $\frac{3}{4}$, $\frac{7}{8}$, 1. Let's count X's per label:
- $\frac{1}{4}$: 3 X's (top three X's? Wait the X's are: first column ( $\frac{1}{4}$ ) has 3 X's (three stacked), then $\frac{1}{2}$ (fourth column) has 2 X's? Wait no, let's re-express all fractions with denominator 8:
  - $\frac{1}{4}=\frac{2}{8}$, $\frac{1}{2}=\frac{4}{8}$, $\frac{3}{4}=\frac{6}{8}$.
  - So labels: $\frac{1}{8}$, $\frac{2}{8}$ ( $\frac{1}{4}$ ), $\frac{3}{8}$, $\frac{4}{8}$ ( $\frac{1}{2}$ ), $\frac{5}{8}$, $\frac{6}{8}$ ( $\frac{3}{4}$ ), $\frac{7}{8}$.
  - Now count X's:
    - $\frac{2}{8}$ ( $\frac{1}{4}$ ): 3 X's (three X's here)
    - $\frac{4}{8}$ ( $\frac{1}{2}$ ): 2 X's (two X's)
    - $\frac{5}{8}$: 1 X? Wait no, looking at the plot: the X's are:
      - At $\frac{1}{4}$ ( $\frac{2}{8}$ ): 3 X's (three vertical X's)
      - At $\frac{1}{2}$ ( $\frac{4}{8}$ ): 2 X's (two X's)
      - At $\frac{5}{8}$: 1 X? Wait no, the X's are: first column ( $\frac{1}{4}$ ) has 3 X's, second column ( $\frac{1}{2}$ ) has 2 X's, third column ( $\frac{5}{8}$ ) has 1 X? Wait no, the original plot: the X's are:
        
        $\frac{1}{4}$: 3 X's (three X's stacked)
        
        $\frac{1}{2}$: 2 X's (two X's)
        
        $\frac{5}{8}$: 1 X? Wait no, the X's are: let's count the number of X's per position:
        
        Position 2 ( $\frac{1}{4}$ ): 3 X's (three X's)
        
        Position 4 ( $\frac{1}{2}$ ): 2 X's (two X's)
        
        Position 5 ( $\frac{5}{8}$ ): 1 X? Wait no, the X's are: total X's: 3 (at $\frac{1}{4}$) + 2 (at $\frac{1}{2}$) + 3 (at $\frac{5}{8}$, $\frac{3}{4}$, $\frac{7}{8}$? No, wait the X's are: first column ( $\frac{1}{4}$ ) 3 X's, second column ( $\frac{1}{2}$ ) 2 X's, third column ( $\frac{5}{8}$ ) 1 X, fourth ( $\frac{3}{4}$ ) 1 X, fifth ( $\frac{7}{8}$ ) 1 X? No, the plot shows:
        
        $\frac{1}{4}$: 3 X's (three X's)
        
        $\frac{1}{2}$: 2 X's (two X's)
        
        $\frac{5}{8}$: 1 X
        
        $\frac{3}{4}$: 1 X
        
        $\frac{7}{8}$: 1 X? No, that can't be. Wait the correct way: let's list each fraction and count X's:
        
        $\frac{1}{4}$: 3 X's (so 3 times $\frac{1}{4}$)
        
        $\frac{1}{2}$: 2 X's (2 times $\frac{1}{2}$)
        
        $\frac{5}{8}$: 1 X (1 time $\frac{5}{8}$)
        
        $\frac{3}{4}$: 1 X (1 time $\frac{3}{4}$)
        
        $\frac{7}{8}$: 1 X (1 time $\frac{7}{8}$)? No, that's not matching. Wait maybe I misread. Let's re-express all fractions with denominator 8:
        
        $\frac{1}{4} = \frac{2}{8}$, $\frac{1}{2} = \frac{4}{8}$, $\frac{3}{4} = \frac{6}{8}$.
        
        So:
        
        $\frac{2}{8}$ ( $\frac{1}{4}$ ): 3 X's → 3 * $\frac{2}{8}$
        
        $\frac{4}{8}$ ( $\frac{1}{2}$ ): 2 X's → 2 * $\frac{4}{8}$
        
        $\frac{5}{8}$: 1 X → 1 * $\frac{5}{8}$
        
        $\frac{6}{8}$ ( $\frac{3}{4}$ ): 1 X → 1 * $\frac{6}{8}$
        
        $\frac{7}{8}$: 1 X → 1 * $\frac{7}{8}$? No, that's too many. Wait the original plot: the X's are:
        
        At $\frac{1}{4}$ ( $\frac{2}{8}$ ): 3 X's (three X's)
        
        At $\frac{1}{2}$ ( $\frac{4}{8}$ ): 2 X's (two X's)
        
        At $\frac{5}{8}$: 1 X
        
        At $\frac{3}{4}$ ( $\frac{6}{8}$ ): 1 X
        
        At $\frac{7}{8}$: 1 X? No, the total X's: 3 + 2 + 1 + 1 + 1 = 8? But a week has 7 days. Wait maybe I made a mistake. Let's look again: the line plot has X's:
        
        First column ( $\frac{1}{4}$ ): 3 X's (three X's)
        
        Second column ( $\frac{1}{2}$ ): 2 X's (two X's)
        
        Third column ( $\frac{5}{8}$ ): 1 X
        
        Fourth column ( $\frac{3}{4}$ ): 1 X? No, that's 3+2+1+1=7? Wait no, the x-axis labels are 0, $\frac{1}{8}$, $\frac{1}{4}$, $\frac{3}{8}$, $\frac{1}{2}$, $\frac{5}{8}$, $\frac{3}{4}$, $\frac{7}{8}$, 1. So positions:
        
        Position 2: $\frac{1}{4}$ → 3 X's
        
        Position 4: $\frac{1}{2}$ → 2 X's
        
        Position 5: $\frac{5}{8}$ → 1 X
        
        Position 6: $\frac{3}{4}$ → 1 X? No, that's 3+2+1+1=7? Wait no, maybe the X's are:
        
        $\frac{1}{4}$: 3 X's (3 days)
        
        $\frac{1}{2}$: 2 X's (2 days)
        
        $\frac{5}{8}$: 1 X (1 day)
        
        $\frac{3}{4}$: 1 X (1 day)? No, 3+2+1+1=7. Yes, 7 days. Now convert all to eighths:
        
        $\frac{1}{4} = \frac{2}{8}$, so 3 * $\frac{2}{8}$ = $\frac{6}{8}$
        
        $\frac{1}{2} = \frac{4}{8}$, so 2 * $\frac{4}{8}$ = $\frac{8}{8}$
        
        $\frac{5}{8}$: 1 * $\frac{5}{8}$ = $\frac{5}{8}$
        
        $\frac{3}{4} = \frac{6}{8}$, so 1 * $\frac{6}{8}$ = $\frac{6}{8}$? Wait no, that's not right. Wait maybe the X's are:
        
        $\frac{1}{4}$: 3 X's (3 * $\frac{1}{4}$)
        
        $\frac{1}{2}$: 2 X's (2 * $\frac{1}{2}$)
        
        $\frac{5}{8}$: 1 X (1 * $\frac{5}{8}$)
        
        $\frac{3}{4}$: 1 X (1 * $\frac{3}{4}$)? No, 3*(1/4) + 2*(1/2) + 1*(5/8) + 1*(3/4). Let's calculate:
        
        3*(1/4) = 3/4 = 6/8
        
        2*(1/2) = 1 = 8/8
        
        1*(5/8) = 5/8
        
        1*(3/4) = 3/4 = 6/8
        
        Total: 6/8 + 8/8 + 5/8 + 6/8 = (6+8+5+6)/8 = 25/8 = 3 1/8? No, that's not. Wait maybe I miscounted X's. Let's try again:
        
        $\frac{1}{4}$: 3 X's (3 days)
        
        $\frac{1}{2}$: 2 X's (2 days)
        
        $\frac{5}{8}$: 1 X (1 day)
        
        $\frac{3}{4}$: 1 X (1 day)? No, 3+2+1+1=7. Wait another approach: list all X's with their fractions:
        
        $\frac{1}{4}$: 3 times → 3*(1/4) = 3/4
        
        $\frac{1}{2}$: 2 times → 2*(1/2) = 1
        
        $\frac{5}{8}$: 1 time → 5/8
        
        $\frac{3}{4}$: 1 time → 3/4
        
        Wait no, that's 3+2+1+1=7? Wait 3*(1/4) = 3/4, 2*(1/2)=1, 1*(5/8)=5/8, 1*(3/4)=3/4. Now sum: 3/4 + 1 + 5/8 + 3/4. Convert to eighths:
        
        3/4 = 6/8, 1 = 8/8, 5/8 = 5/8, 3/4 = 6/8.
        
        Sum: 6/8 + 8/8 + 5/8 + 6/8 = (6+8+5+6)/8 = 25/8 = 3 1/8. Wait 25 divided by 8 is 3 with remainder 1, so 3 1/8. But let's check the options: one of the options is 3 1/8 gallons. Wait but let's re-express the fractions correctly. Wait maybe the X's are:
        
        $\frac{1}{4}$: 3 X's (3 * 1/4)
        
        $\frac{1}{2}$: 2 X's (2 * 1/2)
        
        $\frac{5}{8}$: 1 X (1 * 5/8)
        
        $\frac{3}{4}$: 1 X (1 * 3/4)? No, that's 7 days. Wait another way: maybe the X's are at $\frac{1}{4}$ (3), $\frac{1}{2}$ (2), $\frac{5}{8}$ (1), $\frac{3}{4}$ (1). Wait no, maybe I made a mistake in the fraction labels. Let's look at the x-axis: 0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1. So the positions are:
        
        1/8: 0 X's
        
        1/4: 3 X's
        
        3/8: 0 X's
        
        1/2: 2 X's
        
        5/8: 1 X
        
        3/4: 1 X
        
        7/8: 0 X's
        
        Wait no, that's 3+2+1+1=7. Now calculate:
        
        3*(1/4) = 3/4
        
        2*(1/2) = 1
        
        1*(5/8) = 5/8
        
        1*(3/4) = 3/4
        
        Now sum: 3/4 + 1 + 5/8 + 3/4. Convert to eighths:
        
        3/4 = 6/8, 1 = 8/8, 5/8 = 5/8, 3/4 = 6/8.
        
        Total: 6 + 8 + 5 + 6 = 25 → 25/8 = 3 1/8. Yes, 25 divided by 8 is 3 with 1 remainder, so 3 1/8. So the answer should be 3 1/8 gallons.

Step2: Calculate total

Convert all amounts to eighths:
- $\frac{1}{4} = \frac{2}{8}$, so 3 * $\frac{2}{8}$ = $\frac{6}{8}$
- $\frac{1}{2} = \frac{4}{8}$, so 2 * $\frac{4}{8}$ = $\frac{8}{8}$
- $\frac{5}{8}$: 1 * $\frac{5}{8}$ = $\frac{5}{8}$
- $\frac{3}{4} = \frac{6}{8}$, so 1 * $\frac{6}{8}$ = $\frac{6}{8}$? Wait no, earlier we had 3*(1/4) + 2*(1/2) + 1*(5/8) + 1*(3/4). Wait maybe the X's at $\frac{3}{4}$ are 0? Wait no, the plot shows X's at $\frac{3}{4}$? Wait the original plot: the X's are: first column ( $\frac{1}{4}$ ) 3 X's, second column ( $\frac{1}{2}$ ) 2 X's, third column ( $\frac{5}{8}$ ) 1 X, fourth column ( $\frac{3}{4}$ ) 1 X? No, maybe the X's are:
  - $\frac{1}{4}$: 3 X's
  - $\frac{1}{2}$: 2 X's
  - $\frac{5}{8}$: 1 X
  - $\frac{3}{4}$: 1 X
  - Wait that's 7 X's (3+2+1+1=7). Now sum:
    - 3*(1/4) = 3/4
    - 2*(1/2) = 1
    - 1*(5/8) = 5/8
    - 1*(3/4) = 3/4
    - Now add them: 3/4 + 1 + 5/8 + 3/4. Let's convert to eighths:
      - 3/4 = 6/8, 1 = 8/8, 5/8 = 5/8, 3/4 = 6/8.
      - Sum: 6 + 8 + 5 + 6 = 25 → 25/8 = 3 1/8. Yes, that's 3 and 1/8. So the correct option is 3 1/8 gallons.

Answer:

3$\frac{1}{8}$ gallons (the option with "3$\frac{1}{8}$ gallons")