Question

jen’s goal is to run a total of 22 miles in five days. the table below shows her log for the number of miles she ran on monday, tuesday, wednesday, and friday. how many miles must jen run on friday to reach her goal?
a. $5\frac{7}{8}$
b. $16\frac{1}{8}$
c. 11
d. $11\frac{3}{8}$
jen’s running log

day	distance (miles)
tuesday	$5\frac{1}{8}$
wednesday	0
thursday	$6\frac{1}{4}$
friday	?

Explanation:

Step1: Convert mixed numbers to improper fractions

Monday: \(4\frac{3}{4}=\frac{4\times4 + 3}{4}=\frac{19}{4}\)
Tuesday: \(5\frac{1}{8}=\frac{5\times8+1}{8}=\frac{41}{8}\)
Thursday: \(6\frac{1}{4}=\frac{6\times4 + 1}{4}=\frac{25}{4}\)

Step2: Find a common denominator (8) and add the miles from Monday, Tuesday, Wednesday, and Thursday

Wednesday: 0 miles
Monday (converted to eighths): \(\frac{19}{4}=\frac{19\times2}{4\times2}=\frac{38}{8}\)
Thursday (converted to eighths): \(\frac{25}{4}=\frac{25\times2}{4\times2}=\frac{50}{8}\)
Sum: \(\frac{38}{8}+\frac{41}{8}+0+\frac{50}{8}=\frac{38 + 41+50}{8}=\frac{129}{8}\)

Step3: Subtract the sum from the total goal (22 miles, converted to eighths: \(22=\frac{22\times8}{8}=\frac{176}{8}\))

Friday's miles: \(\frac{176}{8}-\frac{129}{8}=\frac{176 - 129}{8}=\frac{47}{8}=5\frac{7}{8}\)? Wait, no, wait. Wait, the days: Monday, Tuesday, Wednesday, Thursday, Friday. Wait, the table has Monday, Tuesday, Wednesday, Thursday, Friday. Wait, the problem says "the number of miles she ran on Monday, Tuesday, Wednesday, and Friday" – no, wait, the table is Monday, Tuesday, Wednesday, Thursday, Friday. Wait, the question is "How many miles must Jen run on Friday to reach her goal?" So total days: 5 (Monday, Tuesday, Wednesday, Thursday, Friday). So sum of Monday, Tuesday, Wednesday, Thursday, and Friday should be 22. So let's recalculate:

Monday: \(4\frac{3}{4}=\frac{19}{4}\)
Tuesday: \(5\frac{1}{8}=\frac{41}{8}\)
Wednesday: 0
Thursday: \(6\frac{1}{4}=\frac{25}{4}\)
Let \(x\) be Friday's miles. Then \(\frac{19}{4}+\frac{41}{8}+0+\frac{25}{4}+x = 22\)

Convert all to eighths:
\(\frac{19\times2}{8}+\frac{41}{8}+\frac{25\times2}{8}+x=\frac{38 + 41+50}{8}+x=\frac{129}{8}+x = 22\)

\(22=\frac{176}{8}\), so \(x=\frac{176}{8}-\frac{129}{8}=\frac{47}{8}=5\frac{7}{8}\)? But the options have A as \(5\frac{7}{8}\), but the selected option is D. Wait, maybe I misread the days. Wait, the problem says "the number of miles she ran on Monday, Tuesday, Wednesday, and Friday" – no, the table is Monday, Tuesday, Wednesday, Thursday, Friday. Wait, maybe the original problem has a typo, or I misread. Wait, let's check the numbers again.

Wait, Monday: \(4\frac{3}{4}\), Tuesday: \(5\frac{1}{8}\), Wednesday: 0, Thursday: \(6\frac{1}{4}\), Friday: ?

Total goal: 22.

Sum of Monday, Tuesday, Wednesday, Thursday: \(4\frac{3}{4}+5\frac{1}{8}+0 + 6\frac{1}{4}\)

First, add the whole numbers: 4 + 5 + 6 = 15

Add the fractions: \(\frac{3}{4}+\frac{1}{8}+\frac{1}{4}=\frac{3}{4}+\frac{1}{4}+\frac{1}{8}=1+\frac{1}{8}=1\frac{1}{8}\)

Total sum: 15 + 1\(\frac{1}{8}\)=16\(\frac{1}{8}\)

Then Friday's miles: 22 - 16\(\frac{1}{8}\)=21\(\frac{8}{8}\)-16\(\frac{1}{8}\)=5\(\frac{7}{8}\). So the correct answer should be A. But the selected option in the image is D, which is wrong. Wait, maybe I misread the days. Wait, maybe the problem says "Monday, Tuesday, Thursday, and Friday" – no, the table has Wednesday as 0. Wait, maybe the original problem has a different table. Wait, no, the user's image shows Monday: \(4\frac{3}{4}\), Tuesday: \(5\frac{1}{8}\), Wednesday: 0, Thursday: \(6\frac{1}{4}\), Friday: ?

Wait, 4 3/4 is 4.75, 5 1/8 is 5.125, 6 1/4 is 6.25. Sum: 4.75 + 5.125 + 0 + 6.25 = 16.125. 22 - 16.125 = 5.875, which is 5 7/8 (since 7/8=0.875). So 5 7/8 is option A. So the correct answer is A.

Answer:

A. \(5\frac{7}{8}\)