Question

01:59:13

Answer 1

Correct Question:

Stan ran $4\frac{7}{10}$ miles, which was $1\frac{3}{10}$ fewer miles than Matt ran. Four students wrote and solved equations to find m, the number of miles that Matt ran. Which student wrote and solved the equation correctly?

Molly’s work:

$M + 1\frac{3}{10} = 4\frac{7}{10}; M = 5\frac{10}{10} = 6.$

Emma’s work:

$M - 1\frac{3}{10} = 4\frac{7}{10}; M = 3\frac{10}{10} = 4$

Alysa’s work:

$M + 1\frac{3}{10} = 4\frac{7}{10}; M = 3\frac{4}{10} =$ 3 and two-fifths

Maddie’s work:

$M - 1\frac{3}{10} = 4\frac{7}{10}; M = 5\frac{10}{10} = 6$

Answer:

Molly's Work is correct

$M + 1\frac{3}{10} = 4\frac{7}{10}; M = 5\frac{10}{10} = 6.$

Step-by-step explanation:

Let S represent distance covered by Stan and M represent the distance covered by Matt;

Given that the distance covered by Stan is $4\frac{7}{10}$ miles and it is $1\frac{3}{10}$ miles less than that covered by Matt;

This can be represented mathematically as

$S = M - 1\frac{3}{10}$

By substituting $4\frac{7}{10}$ for S;

This gives

$4\frac{7}{10} = M - 1\frac{3}{10}$

By collecting like terms

$4\frac{7}{10} = M - 1\frac{3}{10}$ becomes

$4\frac{7}{10} + 1\frac{3}{10} = M$

Reorder

$M = 4\frac{7}{10} + 1\frac{3}{10}$ ---- This is the correct equation

Solving further to get the distance covered by Matt;

Split fraction

$M = 4 + \frac{7}{10} + 1 + \frac{3}{10}$

Collect like terms

$M = 4 + 1 + \frac{7}{10} + \frac{3}{10}$

$M = 5 + \frac{7}{10} + \frac{3}{10}$

Add fraction (Take LCM)

$M = 5 + \frac{7 + 3}{10}$

$M = 5 + \frac{10}{10}$

Divide Fraction

$M = 5 + 1$

$M = 6$

Hence, the equation of the system is

$M = 4\frac{7}{10} + 1\frac{3}{10}$

and the solution is $M = 6$

Molly’s work is correct