Final answer:
An equation that models the cost of sewing names and instruments for the jazz band is C = 12i + 5l. If 30 instruments must be sewn, the band can afford to sew 228 letters.
Step-by-step explanation:
To model the situation where your jazz band can spend $1,500 to sew members' names and instruments on their jackets with the sewing cost of $12 per instrument and $5 per letter, we can write the equation:
C = 12i + 5l
where C represents the total cost, i represents the number of instruments, and l represents the total number of letters.
The total budget for sewing is $1,500, so we set the equation to equal $1,500:
1500 = 12i + 5l
If 30 instruments must be sewn (i = 30), we plug this into the equation to find the number of letters (l) the band can afford to sew:
1500 = 12(30) + 5l
1500 = 360 + 5l
1500 - 360 = 5l
1140 = 5l
l = 1140 / 5
l = 228
Therefore, the band can afford to sew 228 letters.