Before beginning voice lessons, Elizabeth already knew how to sing 15 pieces, and she expects to learn 2 new pieces during each week of lessons. How many weeks of lessons will Elizabeth need before she will be able to sing a total of 47 pieces?

Question

Noah Archer · Accepted Answer

16 weeks.

The first step is to find out how many more pieces she needs to learn 47 pieces - 15 pieces ( that she already knows = 32 pieces left to learn She learns 2 pieces per week, per means to divide so divide 32 by 2 # 32/2 = 16 # It will take 16 weeks for her to learn the 32 new pieces she needs to reach the desired 47 pieces

Emery Allen · Answer

So the number of weeks to learn 32 more songs is 16

#color(blue)("Preamble")# Consider the example of #3/4# this can be written as #6/8# and have the same value. It just looks different. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering your question")# Total to know# ->47# Already know#->ul(15) larr" subtract"# Need to learn#->32# Using ratio: #"Given values for ratio"->("learn count")/("week count") -> 2/1# But we need to learn 32 so we have #("learn count")/("week count") -> 2/1 -=32/("week count")# Note that #-=# means 'equivalent to' #color(brown)("Multiply by 1 and you do not change the overall value. However, 1")##color(brown)("comes in many forms.")# #("learn count")/("week count") -> [2/1 color(magenta)(xx1 )]-=32/("week count")# #" "[2/1color(magenta)(xx16/16)]=32/("weeks count")# #" "[32/16]=32/("weeks count")# So the number of weeks to learn 32 more songs is 16

Aurora Arias · Answer

undefined To find out how many weeks of lessons Elizabeth will need to sing a total of 47 pieces, we can set up an equation:

Let $ x $ represent the number of weeks of lessons Elizabeth will need.

Given that she already knows how to sing 15 pieces and expects to learn 2 new pieces each week, the total number of pieces she will know after $ x $ weeks can be represented as $ 15 + 2x $.

We want this total to be equal to 47:

$$ 15 + 2x = 47 $$

Now, solve for $ x $:

$$ 2x = 47 - 15 $$
$$ 2x = 32 $$
$$ x = \frac{32}{2} $$
$$ x = 16 $$

Therefore, Elizabeth will need 16 weeks of lessons before she will be able to sing a total of 47 pieces.