Question

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?
$m = 101 - 21d$
$m = 108 - 3d$
$m = 72 - 15d$
$m = 90 - 6d$

Explanation:

Step1: Analyze the problem

We need to find the equation for the number of measures \(m\) Harita still needs to memorize as a function of \(d\) (days of practice). The initial number of measures is \(90\) (since she must memorize \(90\) in total), and she memorizes \(18\) new measures every \(3\) days.

Step2: Calculate the rate of memorization per day

The rate \(r\) (measures per day) is \(\frac{18}{3}=6\) measures per day.

Step3: Form the linear equation

Using the slope - intercept form \(y = mx + b\) (here \(m\) is the number of measures left, \(x=d\), slope \(=- 6\) (negative because the number of measures left decreases as days increase), and \(b = 90\) (initial number of measures). So the equation is \(m=90 - 6d\).

Answer:

\(m = 90-6d\)