To determine how many days it would take for Nicholas to collect 2600 cans, we start with the given equation:
[tex]\[ y = 235x + 15 \][/tex]
Here, [tex]\( y \)[/tex] represents the total number of cans collected, and [tex]\( x \)[/tex] represents the number of days. We need to find the value of [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is 2600.
1. Substitute [tex]\( y \)[/tex] with 2600 in the equation:
[tex]\[ 2600 = 235x + 15 \][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
To do this, we first subtract 15 from both sides of the equation:
[tex]\[ 2600 - 15 = 235x \][/tex]
[tex]\[ 2585 = 235x \][/tex]
3. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we divide both sides of the equation by 235:
[tex]\[ x = \frac{2585}{235} \][/tex]
4. Calculate the result:
Performing the division:
[tex]\[ x = 11 \][/tex]
Therefore, it would take 11 days for Nicholas to collect 2600 cans.
