Question

Solve the equation w−5 2/5=3 1/4
.(1 point)
Responses

w=8320
w equals 8 Start Fraction 3 over 20 end fraction

w=81320
w equals 8 Start Fraction 13 over 20 end fraction

w=2320
w equals 2 Start Fraction 3 over 20 end fraction

w=839
w equals 8 Start Fraction 3 over 9 end fraction

Answer 1

To solve the equation \( w - 5 \frac{2}{5} = 3 \frac{1}{4} \), we first convert the mixed numbers into improper fractions:

1. Convert \( 5 \frac{2}{5} \):
\[
5 \frac{2}{5} = 5 + \frac{2}{5} = \frac{25}{5} + \frac{2}{5} = \frac{27}{5}
\]

2. Convert \( 3 \frac{1}{4} \):
\[
3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}
\]

Now, substitute these values back into the equation:
\[
w - \frac{27}{5} = \frac{13}{4}
\]

Next, add \( \frac{27}{5} \) to both sides:
\[
w = \frac{13}{4} + \frac{27}{5}
\]

To add these fractions, we need a common denominator. The least common multiple of 4 and 5 is 20. Convert both fractions:

- Convert \( \frac{13}{4} \):
\[
\frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20}
\]

- Convert \( \frac{27}{5} \):
\[
\frac{27}{5} = \frac{27 \times 4}{5 \times 4} = \frac{108}{20}
\]

Now add the two fractions:
\[
w = \frac{65}{20} + \frac{108}{20} = \frac{65 + 108}{20} = \frac{173}{20}
\]

Now, let's express this as a mixed number:
\[
\frac{173}{20} = 8 \frac{13}{20}
\]

Thus, the solution is:
\[
w = 8 \frac{13}{20}
\]

So the answer is:
\[
w = 8 \frac{13}{20}
\]