To determine the equation that shows the number of measures [tex]\( m \)[/tex] Harita still needs to memorize as a function of [tex]\( d \)[/tex] days of practice:
1. Identify the total number of measures Harita needs to memorize: [tex]\( 90 \)[/tex] measures.
2. Identify the number of measures she memorizes over a set period: Harita memorizes [tex]\( 18 \)[/tex] measures every [tex]\( 3 \)[/tex] days.
3. Determine the number of measures memorized per day:
[tex]\[
\text{Measures per day} = \frac{\text{Measures per 3 days}}{3} = \frac{18}{3} = 6 \text{ measures per day}
\][/tex]
4. Define the relationship between the number of days [tex]\( d \)[/tex] and the number of measures memorized:
If Harita memorizes [tex]\( 6 \)[/tex] measures per day, then after [tex]\( d \)[/tex] days, she will have memorized [tex]\( 6d \)[/tex] measures.
5. Formulate the equation for the number of measures left to memorize:
Harita started with [tex]\( 90 \)[/tex] measures, and she reduces this by the number of measures she has memorized after [tex]\( d \)[/tex] days:
[tex]\[
m = 90 - 6d
\][/tex]
Here,
- [tex]\( 90 \)[/tex] is the initial total number of measures.
- [tex]\( 6d \)[/tex] is the number of measures she has memorized after [tex]\( d \)[/tex] days.
6. Verify the options provided:
- [tex]\( m = 72 - 15d \)[/tex]
- [tex]\( m = 90 - 6d \)[/tex]
- [tex]\( m = 101 - 21d \)[/tex]
- [tex]\( m = 108 - 3d \)[/tex]
The correct equation that represents the number of measures Harita still needs to memorize, given she memorizes 6 measures per day, is:
[tex]\[
m = 90 - 6d
\][/tex]
