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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 [tex]\( m \)[/tex], the number of measures she still needs to memorize, as a function of [tex]\( d \)[/tex], the number of days of practice since she began learning the piece?

A. [tex]\( m = 72 - 15d \)[/tex]
B. [tex]\( m = 90 - 6d \)[/tex]
C. [tex]\( m = 101 - 21d \)[/tex]
D. [tex]\( m = 108 - 3d \)[/tex]



Answer :

GinnyAnswer
To find the correct equation that represents the number of measures Harita still needs to memorize after `d` days of practice, let's follow the given scenario step by step.

1. Total Measures:
Harita needs to memorize a total of 90 measures.

2. Memorization Rate:
Harita memorizes 18 measures every 3 days. To find the rate at which she memorizes measures per day, we can calculate:

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

3. Formulating the Equation:
Let [tex]\( d \)[/tex] represent the number of days of practice. After [tex]\( d \)[/tex] days, the number of measures Harita has memorized can be calculated as:

[tex]\[ \text{Measures memorized} = 6d \][/tex]

4. Remaining Measures:
To determine the number of measures she still needs to memorize ([tex]\( m \)[/tex]), subtract the measures she has already memorized from the total measures:

[tex]\[ m = 90 - 6d \][/tex]

Therefore, the correct equation that represents the number of measures Harita still needs to memorize after [tex]\( d \)[/tex] days of practice is:

[tex]\[ m = 90 - 6d \][/tex]

Among the given options, the correct one is:

[tex]\[ m = 90 - 6d \][/tex]

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