Question
He has already picked 1 and one-fourth bushels and picks at a rate of StartFraction 7 Over 8 EndFraction of a bushel each hour. The equation StartFraction 7 Over 8 EndFraction h + 1 and one-fourth = 6 can be used to represent h, the number of hours it will take him to pick 6 bushels. What is the value of h?
4 and StartFraction 5 Over 32 EndFraction hours
5 and StartFraction 3 Over 7 EndFraction hours
5 and StartFraction 17 Over 28 EndFraction hours
8 and StartFraction 2 Over 7 EndFraction hours
4 and StartFraction 5 Over 32 EndFraction hours
5 and StartFraction 3 Over 7 EndFraction hours
5 and StartFraction 17 Over 28 EndFraction hours
8 and StartFraction 2 Over 7 EndFraction hours
Answers
GPT-4o mini
To solve for \( h \) in the equation
\[
\frac{7}{8}h + 1\frac{1}{4} = 6,
\]
we first convert \( 1\frac{1}{4} \) into an improper fraction:
\[
1\frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}.
\]
Now we can rewrite the equation:
\[
\frac{7}{8}h + \frac{5}{4} = 6.
\]
Next, let's isolate \( \frac{7}{8}h \) by subtracting \( \frac{5}{4} \) from both sides:
\[
\frac{7}{8}h = 6 - \frac{5}{4}.
\]
To perform the subtraction, we first convert 6 into a fraction with a denominator of 4:
\[
6 = \frac{24}{4}.
\]
Now we can subtract:
\[
\frac{7}{8}h = \frac{24}{4} - \frac{5}{4} = \frac{19}{4}.
\]
Now we need to solve for \( h \) by multiplying both sides by the reciprocal of \( \frac{7}{8} \), which is \( \frac{8}{7} \):
\[
h = \frac{19}{4} \times \frac{8}{7}.
\]
Now we multiply:
\[
h = \frac{19 \cdot 8}{4 \cdot 7} = \frac{152}{28}.
\]
We can simplify \( \frac{152}{28} \):
\[
\frac{152 \div 4}{28 \div 4} = \frac{38}{7}.
\]
To convert \( \frac{38}{7} \) into a mixed number, we perform the division:
\[
38 \div 7 = 5 \quad \text{with a remainder of } 3,
\]
which gives us:
\[
\frac{38}{7} = 5\frac{3}{7}.
\]
Thus, the value of \( h \) is
\[
\boxed{5 \frac{3}{7}} \text{ hours}.
\]
\[
\frac{7}{8}h + 1\frac{1}{4} = 6,
\]
we first convert \( 1\frac{1}{4} \) into an improper fraction:
\[
1\frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}.
\]
Now we can rewrite the equation:
\[
\frac{7}{8}h + \frac{5}{4} = 6.
\]
Next, let's isolate \( \frac{7}{8}h \) by subtracting \( \frac{5}{4} \) from both sides:
\[
\frac{7}{8}h = 6 - \frac{5}{4}.
\]
To perform the subtraction, we first convert 6 into a fraction with a denominator of 4:
\[
6 = \frac{24}{4}.
\]
Now we can subtract:
\[
\frac{7}{8}h = \frac{24}{4} - \frac{5}{4} = \frac{19}{4}.
\]
Now we need to solve for \( h \) by multiplying both sides by the reciprocal of \( \frac{7}{8} \), which is \( \frac{8}{7} \):
\[
h = \frac{19}{4} \times \frac{8}{7}.
\]
Now we multiply:
\[
h = \frac{19 \cdot 8}{4 \cdot 7} = \frac{152}{28}.
\]
We can simplify \( \frac{152}{28} \):
\[
\frac{152 \div 4}{28 \div 4} = \frac{38}{7}.
\]
To convert \( \frac{38}{7} \) into a mixed number, we perform the division:
\[
38 \div 7 = 5 \quad \text{with a remainder of } 3,
\]
which gives us:
\[
\frac{38}{7} = 5\frac{3}{7}.
\]
Thus, the value of \( h \) is
\[
\boxed{5 \frac{3}{7}} \text{ hours}.
\]