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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 Harita 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
Let's solve the problem step-by-step to find the equation that determines the number of measures Harita still needs to memorize as a function of the number of days of practice since she began learning the piece.

1. Initial Information:
- Harita needs to memorize a total of 90 measures of music.
- She plans on memorizing 18 new measures every 3 days.

2. Rate of Memorization:
- To determine the daily rate of memorization, we divide the total measures of music memorized in 3 days by the number of days:
[tex]\[ \text{Measures per day} = \frac{18 \text{ measures}}{3 \text{ days}} = 6 \text{ measures per day} \][/tex]

3. Derive the Equation:
- Let [tex]\( d \)[/tex] be the number of days of practice.
- The total number of measures Harita memorizes after [tex]\( d \)[/tex] days can be found by multiplying the daily memorization rate by [tex]\( d \)[/tex]:
[tex]\[ \text{Measures memorized after } d \text{ days} = 6d \][/tex]
- The number of measures she still needs to memorize is the initial total measures minus the measures she has already memorized:
[tex]\[ m = 90 - 6d \][/tex]

4. Conclusion:
- The equation that represents the number of measures Harita still needs to memorize as a function of the number of days of practice is:
[tex]\[ m = 90 - 6d \][/tex]

Therefore, the correct equation is:
[tex]\[ m = 90 - 6d \][/tex]

Among the given options, this corresponds to:
[tex]\[ m = 90 - 6d \][/tex]

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