Grace and Drew do volunteer work at the animal shelter. Drew worked 3 hours more than Grace, and together they worked more than 27 hours. Complete the inequalities to show how many hours each worked.

Answer 1

Let's denote the number of hours Grace worked as \( g \) and the number of hours Drew worked as \( d \).

According to the problem, we have two pieces of information:

1. Drew worked 3 hours more than Grace: \[ d = g + 3 \]

2. Together, they worked more than 27 hours: \[ g + d > 27 \]

Now, we can substitute the expression for \( d \) from the first equation into the second inequality:

\[ g + (g + 3) > 27 \]

Simplifying this gives:

\[ 2g + 3 > 27 \]

Now, subtract 3 from both sides:

\[ 2g > 24 \]

Finally, divide by 2:

\[ g > 12 \]

Now, since \( d = g + 3 \), we can express Drew's work in terms of Grace's work:

\[ d > 12 + 3 \] \[ d > 15 \]

Thus, the inequalities that represent the number of hours each worked are:

• For Grace: \[ g > 12 \]

• For Drew: \[ d > 15 \]