Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?

Question

m = 72 – 15d
m = 90 – 6d
m = 101 – 21d
m = 108 – 3d

Answer 1

To find the equation that relates the number of measures Harita still needs to memorize, \( m \), as a function of the number of days of practice, \( d \), we start by analyzing the information given.

Harita needs to memorize a total of 90 measures. She memorizes 18 new measures every 3 days.

First, we can calculate how many measures she memorizes per day:

\[ \text{Measures per day} = \frac{18 \text{ measures}}{3 \text{ days}} = 6 \text{ measures per day} \]

Next, we can write an expression for the number of measures she has memorized after \( d \) days of practice. If she memorizes 6 measures each day, then after \( d \) days, she has memorized:

\[ 6d \text{ measures} \]

Now, to find the number of measures still to be memorized \( m \), we subtract the number of measures she has memorized from the total number of measures:

\[ m = 90 - 6d \]

This matches the second option from the given equations:

\[ m = 90 - 6d \]

So, the correct equation is:

\[ \text{m = 90 - 6d} \]