Guitar Practice You practice playing your guitar every day. You spend 15 minutes practicing chords and the rest of the time practicing a new song. So the total number of minutes y you practice for the week is given by y 5 7(15 1 x), where x is the number of minutes you spend on practicing a new song.
a. Solve the equation for x.
b. How many minutes did you spend on a new song if you practiced 210 minutes last week? 245 minutes? 315 minutes?
An equation needs an equal (=) sign. Where is yours?
To solve the equation for x, we can start by expanding the expression inside the parentheses:
y = 5(7(15 + x))
Now we can simplify the equation by distributing the multiplication:
y = 5(105 + 7x)
Next, we can distribute the multiplication again:
y = 525 + 35x
To solve for x, we need to isolate the variable. We can do this by subtracting 525 from both sides of the equation:
y - 525 = 35x
Finally, we can divide both sides of the equation by 35:
x = (y - 525) / 35
Now let's solve for x using the given values:
a. If you practiced 210 minutes last week:
x = (210 - 525) / 35
x = -315 / 35
x = -9 minutes (rounded to the nearest whole number)
b. If you practiced 245 minutes last week:
x = (245 - 525) / 35
x = -280 / 35
x = -8 minutes (rounded to the nearest whole number)
c. If you practiced 315 minutes last week:
x = (315 - 525) / 35
x = -210 / 35
x = -6 minutes (rounded to the nearest whole number)
Note that a negative value for x indicates that you spent less than 15 minutes on practicing chords, which might not be possible or practical in this context.