# Mrs. Roberts sewed m shirts using 2 yards of cloth for each shirt. She also sewed (m + 2) dresses, using 5 yards of cloth for each dress. How much cloth did she use altogether?

Apr 26, 2017

See the solution process below:

#### Explanation:

We can write the expression for how much cloth Mrs. Roberts used for the shirts as:

${c}_{s} = m \cdot 2$

Where ${c}_{s}$ is the cloth Mrs. Roberts used for the shirts and $m$ is the number of shirts Mrs. Roberts sewed.

We can write the expression for how much cloth Mrs. Roberts used for the dresses as:

${c}_{d} = \left(m + 2\right) \cdot 5$

Where ${c}_{d}$ is the cloth Mrs. Roberts used for the dresses and $m + 2$ is the number of shirts Mrs. Roberts sewed.

We can now write the formula for how much cloth Mrs. Roberts used altogether as:

$c = {c}_{s} + {c}_{d}$

Substituting and solving for $c$ gives:

$c = \left(m \cdot 2\right) + \left(\left(m + 2\right) \cdot 5\right)$

c = 2m + ((5 * m) + (5 * 2)

$c = 2 m + \left(5 m + 10\right)$

$c = 2 m + 5 m + 10$

$c = \left(2 + 5\right) m + 10$

$c = 7 m + 10$

Altogether Mrs. Roberts use $7 m + 10$ yards of cloth.